Physics Unit 1: Forces and Motion
What is the equation for uniformly accelerated motion?
(final speed)^2 = (initial speed)^2 + (2 x acceleration x distance moved) v^2 = u^2 + 2as
A railway truck with a mass of 5000 kg rolling at 3 m/s collides with a stationary truck of mass 10,000 kg. The trucks join together. At what speed do they move after the collision? We assume that the friction forces re small enough to ignore so we can apply the law of conservation of momentum: momentum before the collision = momentum after the collision
(mass a x velocity a) + (mass b x velocity b) = (mass a x velocity c)+ (mass b x velocity d) (5,000 x 3) + (10,000 x 0 ) = (10,000 x velocity b) + (5,000 x velocity c) 15,000 = 10,000 + 5,000 x v 15,000 = 15,000 v 15000 / 15000 = v v = 1 After the collision the trucks move with a velocity of 1 m/s in the same direction that the original truck was traveling
What is the relationship between: 1. MN and N 2. Tonnes and kilograms
1. 1 MN - 1,000,000 N 2. 1 tonne - 1000 kg
How many: 1. Grams (g) 2. Milligrams (mg) Are in a kilogram?
1. 1,000,000 2. 1,000
How many meters are in a: 1. Kilometre (km) How many: 2. Centimetres (cm) 3. Millimetres (cm) Are in a metre?
1. 1000 m 2. 100 cm 3. 1000 mm
Average speed calculation example: 1. A car travels 100 kilometers in 2 hours
1. 50 km/h If you look at the speedometer of a car, you will see that the speed changes from instant to instant as the accelerator or brake is used. Therefore, the speedometer shows the instantaneous speed of the car (the speed in that moment)
Analyzing the results of the force, mass and acceleration experiment?
1. In a graph plotting acceleration against force where the mass of the trolley and the hanging masses are constant, but the force is changed by moving around the masses, the graph is linear and passes through the origin This shows that force is proportional to acceleration Therefore, doubling the force acting on an object double the acceleration 2. Alternatively, if the position of the masses is kept constant but the mass of the trolley is varied, then the graph is linear when acceleration is plotted against 1/m Therefore, acceleration is inversely proportional to mass This means that for a given unbalanced force acting on an object, doubling its mass will halve the acceleration Combining these results gives us: Force (N) = mass (kg) x acceleration (m/s^2) F = m x a
What are the units for speed?
1. meter per second 2. kilometer per hour 3. centimeters per second To convert m/s to km/h multiply by 3.6 To convert m/s to cm/s multiply by 1000 The rule is simply multiply by whatever has changed: Multiply to get a larger time: v (m/s) x 60 (to get meters per minute) x 60 (to get meters per hour) then Divide to get a larger length: v (m/h) / 1000 = v (km/h)
What is the unit for: 1. Torque 2. Momentum 3. Mass 4. Length 5. Time 6. Speed/velocity 7. Acceleration 8. Force 9. Gravitational field strength
1. newton meter (N m) 2. kilogram meter per second (kg m/s) 3. kilogram (kg) 4. metre (m) 5. second (s) 6. metre per second (m/s) 7. metre per second squared (m/s2) 8. newton (N) 9. newton per kilogram (N/kg)
There is a wooden metre ruler with a mass of 0.12 kg. A pivot at the 40 cm mark supports the ruler. When a brass weight is placed at the 20cm mark the ruler just balances in the horizontal position Take moments about the pivot to calculate the mass of the brass weight
100 cm long Pivot at 40 cm brass weight at 20 cm Centre of gravity is 10 cm away from the pivot 20 x m = 0.12 x 10 20m x 1.2 m = 0.06
What is deceleration?
A decelerating object is slowing down which means that it has a smaller final velocity than its starting velocity. If you use the equation for finding acceleration of an object that is slowing down, the answer is negative.
How can we conduct an experiment with low friction?
A linear air track reduces friction dramatically The friction is so low that the object moves at a constant velocity and doesn't slow down
Practical: Investigate the motion of everyday objects such as toy cars or tennis balls?
A raised wooden runway can be set up to investigate the motion of a toy car. Safety: these should be stacked and moved carefully and used at a low level so that they don't fall. If heavy trolleys are used as vehicles, a catch box filled with bubble wrap should be placed at the end of the runway 1. Firstly, you need to measure the height of the raised end of the wooden track The track should be securely clamped at the height under test and the height should always be measured using a metre ruler perpendicular to the bench surface You must always measure to the same point on the raised end of the track. This is called the fiducial mark 2. To find the average speed you will need to use the equation: average speed (v) = distance moved (s) / time taken (t) So you will need to measure the distance AB with a meter ruler and then measure the time it takes for the car to travel this distance with a stop watch When timing the stop watch, human reaction time will introduce measurement error. To make these smaller the time to travel distance AB should, for a given value of h, be measured at least three times and an average value found You should always start from point A and if a vastly different value is found it should be excluded and treated as anomalous (inaccurate) 3. You can write a table displaying the three time results for a particular height as well as the average time and average speed In some exams you will be required to complete a table using the necessary calculations or to plot a graph and then draw a conclusion. Conclusions must be explained in reference to the graph For example, if the points plotted form a straight line and it passes through the origin then it can be concluded that there is a proportional relationship between the distance and time and therefore the speed is constant
How can we investigate friction?
A simple system involving two surfaces and weights can be used to investigate friction. One surface will be in a plank form and have a pulley attached on the end. The other will be a smaller test block with a weight on it to vary the normal reaction force that's attached to the pulley. The pulley has a weight on the end. A "catch box" filled with bubble wrap under the suspended masses keeps hand and feed out of harm. The weight force on the line running over the pulley pulls the block horizontally along the track and friction acts on the block to oppose this force. The weight is increased until the block just starts to move; this happens when the pull of the weight force just overcomes the friction force. The friction force between the block and the track has maximum value The apparatus can be used to test different factors that can affect the size of the friction force: 1. The smoothness of the surface- every surface has hills and valleys. Smooth surfaces have less steep hills and valleys meaning they are less likely to interlock. As the objects interlock, more kinetic energy is converted to heat energy 2. The mass of the object- the greater the mass, the greater the gravitational force pulling it downwards, the greater the friction
Practical: Investigate how the extension of a spring changes with load?
A spring with a load attached to it is hung off of a clamp on a ring stand The length of the unstretched spring is measured before the force is applied to it with a ruler and then the spring is loaded with different weights The extension for each load is measured against a scale using a set square to improve measurement accuracy A table of results is recorded and a graph of force as the y axis against extension as the x axis is drawn Eye protection should be worn for this experiment in case the spring comes loose, the stands should be clamped to the table and attention should be paid to hand and feet especially with heavy loads
Describe an experiment involving force, mass and acceleration?
A trolley can be set up on a slightly sloping ramp. The slope of the ramp is adjusted so that the trolley keeps moving down if you push it gently. The slope is intended to reduce the friction in the trolley's wheels The force acting on the trolley is provided by the masses on the end of a nylon line sliding over a pulley system as well as masses on top of it The masses at the end of the nylon line accelerate as well as the trolley, so the force is increased by transferring one of the masses from the trolley to the mass hanger. This is because this increases the pulling force on the trolley whilst keeping the total mass of the system the same. The acceleration of the trolley can be measured by taking a series of pictures at equal time intervals using a digital video camera. Alternatively, the previously mentioned light gates and data logger can be used to find the speed of the trolley near the end of the runway and near the beginning of the runway Then the equation for acceleration can be used: acceleration = final speed - initial speed / time Safety note: heavy wooden runways need to be stacked and moved carefully. They are best used at a low level rather than being placed on benches or tables where they may fall off If heavy trolleys are used a catch box filled with bubble wrap or a similar material should be placed at the end of the runway
What is the equation for acceleration?
Acceleration = change in velocity / time taken or final velocity - initial velocity / time taken a = (v-u) / t The unit "u" is used for initial velocity because it comes before "v"!
How does an airplane depend on unbalanced forces?
Air crafts must accelerate to a very high speed in a very short amount of time when taking off and decelerate quickly when landing back on the aircraft carrier The unbalanced force on the plane causes the acceleration The forces that act horizontally on the plane are the friction force between the wheels and the flight deck and air resistance when the aircraft starts to move At the start, the forward thrust of the aircraft engines is much greater than air resistance and friction so there is a large unbalanced force to cause acceleration When the aircraft lands on the flight deck it must decelerate to stop in a short distance so parachutes and drag wires are used to provide a large unbalanced force acting in the opposite direction to the its movement
What is an object in balance?
An object in balance will not try to turn around a pivot point: sum of anti clockwise moments = sum of clockwise moments If on a see saw the anti clockwise moment is = 200 N x 1.5 m = 300 Nm and the clockwise moment is = 300 x 1.5 = 450 Nm Then the see saw is not balanced and will lean down to the right as it rotates clockwise around the pivot This calculation is approximate because the forces are not acting perpendicularly to the see saw If then the mass of 300 N moves closer so that it is 1.0 m away from the pivot, the moments will be equal and the see saw will be balanced
What is air resistance and terminal velocity?
An object moving through air experiences a force that opposes its motion called air resistance or drag The size of the drag force acting on an object depends on its shape and speed The drag coefficient is a measure of how easily an object moves through the air Cars are designed to have a low drag coefficient and so are high speed trains. They have a streamlined shape so that airs flows more easily around them It is particularly important to make fast moving objects streamlined because the drag force increases with the speed of the object The fact that drag increases with speed affects the way that dropped objects accelerate because the faster they move the greater the drag opposing their motion becomes Objects falling through air experience two significant forces; the weight force (the pull of gravity on the object) and the opposing drag force When a ball is dropped: a) At the point of release the velocity and drag are both zero. The only force acting on the ball is weight. This causes the ball to accelerate towards Earth b) Now the ball accelerates meaning that the velocity and therefore drag are increasing. The acceleration is less though because of the opposing forces. However, at this point the weight force is larger than the drag force. The more the ball accelerates, the greater the drag. c) The ball reaches terminal velocity meaning that the drag force and the weight are equal so the acceleration is zero. Although the ball is still falling, it is not getting any faster
What is the relationship between force, mass and acceleration?
An object will not change its velocity unless there is an unbalanced force acting on it If a car is traveling on the motorway at a constant speed, it is being pushed along by a force from its engine which is needed to balance the forces of friction and air resistance acting on the car At a constant speed, the unbalanced force on the car is zero If there are unbalanced forces acting on an object, the object can accelerate or decelerate depending on the direction of the unbalanced force The acceleration depends on the size of the unbalanced forces and the mass of the object If the same force is applied to two objects, one with a large mass and one with a small mass, the object with the smaller mass will have a larger acceleration If two different magnitudes of force are applied to two objects with the same mass, the larger force will cause a large acceleration and the small force will cause a small acceleration
Practical: opening a door
Challenge a partner to try to hold a door closed while you try and open it They can apply a pushing force but no further than 20 cm from the hinge while you try to pull the door open but pulling on the handle. You should be able to open the door quite easily You will realize that you have an advantage because the turning effect of your force doesn't just depend on the size of the force you apply but also on the distance from the hinge or pivot at which you apply it You have the advantage of greater leverage
How can we carry out Galileo's experiment using more modern equipment?
Data loggers can be used to make accurate direct measurements that are collected and analyzed by a computer A spreadsheet program can be used to make a velocity time graph This experiment is conducted using a slider on a slightly sloping air track. The air track reduced friction because the glider rides on a cushion of air that is pushed continuously through the holes along the air track As the glider accelerates down the sloping track the card stuck on it breaks a light beam and the time that the slider takes to pass it is measured electronically If the length of the card is measured, this is entered into a spreadsheet to compute the velocity of the glider at different points using the equation: v = s / t This alongside the interval times can be used to create a velocity time graph The experiment can be repeated with different heights of slopes
How do elastic bands behave when a load is applied to them?
Elastic bands are usually made of rubber You can use the same apparatus for the spring experiment but replace the spring with an elastic If you stretch an elastic band with increasing load forces, you get a graph that isn't a straight line, showing it they doesn't comply with Hooke's law
What is the equation relating force to mass and acceleration?
Force (N) = mass (kg) x acceleration (m/s^2) F = m x a
A car traveling at 20 m/s collides with a stationary lorry and is brought to a rest in just 0.02 s. A woman in the car has a mass of 50 kg. She experiences the same deceleration when she comes into contact with a hard surface in the car. What force does the person experience?
Force = change in momentum / time Momentum = mass x velocity Force = (20 x 50) - (0 x 50) / 0.02 Force = 1000 - 0 / 0.02 Force = 1000 / 0.02 Force = 50, 000 N
What kind of quantity is force?
Force is a vector quantity because it's connected to both magnitude and direction
What are forces?
Forces are pushes and pulls of one thing on another
How do the shapes of objects change with force?
Forces are what set things in motion, get them to accelerate or decelerate Sometimes the change of shape in an object is temporary like the suspension spring in a mountain bike Sometimes the shape of the object is permanently changed like a crushed can or car that has collided with another object A temporary change of shape can provide a useful way of absorbing and storing energy like the spring in a clock Permanent changes can result in the failure of a structure to support a load
What are some examples of forces?
Friction - a force that opposes motion Reaction force - a force that opposes gravity and creates an upwards push Weight / gravitational force - a force that pulls objects into the Earth's core Magnetic force - the forces of attraction or repulsion between two magnetic objects For example, magnetic forces are used for moving compass needles, rotating electric motors, holding fridge doors shut etc. Electrostatic force - the attractive or repulsive force between two electrically charged objects For example, this is seen when your hair sticks to the comb after brushing it or when touching a Van de Graaf generator Air resistance or drag - and upward force that opposes movement of objects through the air For example, parachutes cause parachutists to descend more slowly and designer cars, high speed trains and other fast moving objects try to reduce this force by becoming sleeker. Marine animals are more streamlines to reduce these forces in water Upthrust - this is the upward push of air in spite of gravity For example, hot air ballon move upwards and this force also acts on objects in water Nuclear forces - the attractive forces in the nucleus
What is friction?
Friction is the force that causes moving objects to slow down and finally stop The kinetic energy of the moving object is transferred to heat as work is done by the friction force For ice skaters for example, the force of friction is very small so they are able to glide long distances without having to do any work. This is also the force that allows a car's wheels to grip to the road and make it accelerate very quickly Scientists have worked hard for many years to develop materials that increase and reduce friction Reducing friction means that the machines work more efficiently (waste less energy) and don't wear out so quickly Increasing friction helps to make tires that grip the road better and to make more effective brakes Friction occurs when solid objects rub against other solid objects or when objects move through fluids (liquids and gases) Sprint cyclists and olympic swimmers wear special materials to reduce the effects of fluid friction so they can achieve faster times in their races Sometimes fluid friction is desirable - for example when someone using a parachute after jumping from a plane (drag)
What is Hooke's Law?
Hooke measured the increase in length (extension) produced by different load forces on springs The graph he obtained by plotting force against extension was a straight line passing through the origin This shows that the extension of the spring is proportional to the force Hooke's law also applies to wires. If you stretch a wire, you will find that the extension is proportional to the load up to a certain load and then it may behave like a spring past its elastic limit Wires made of different metals behave in different ways. Some obey Hooke's law until the wire breaks and other stretch elastically and then plastically before breaking When they stretch plastically they don't return to their original length once the force is removed and may show signs of narrowing or "necking"
When doesn't Hooke's law apply?
Hooke's law doesn't apply if you stretch the spring too far On the graph the line stops being linear and starts to curve at a point called the limit of proportionality This is the point where the spring stops obeying Hooke's law and starts to stretch more for each increase in the load force If the load is increased more, a point called the elastic limit is reached Once you have stretched a spring beyond the elastic limit it will not return to its original length as you take the weights off the spring
How do forces act on a beam?
If a boy stands on a beam over a lake, the upward forces on the beam are equal to the force of his weight (400 N) a) If he stands in the middle of the beam, the reaction force is equal at both ends (200 N) b) If he stands at the end of the beam, the reaction force will be 400 N at the end of the beam c) If he stands three quarters of the way across the beam, the reaction force will be 300 N on the end of the beam he is closest to and 100N on the end of the beam he is furthest away from
What happens when objects are not pivoted at the centre of gravity?
If objects are not pivoted at the centre of gravity there will be a turning effect
Which materials change shape temporarily?
If you apply a force to an elastic band, its shape changes; the band stretches and gets longer All materials will stretch a little when you put them under tension or shorten when you compress them You can stretch a rubber band easily but a huge force is needed to cause a noticeable extension in a piece of steel of the same length Some materials, like glass, don't change shape easily and are brittle so they break rather than noticeably stretching Elastic materials don't break easily and tend to return to their original shape when forces acting on them are removed Other materials like clay are not elastic but plastic; they change shape when even small forces are applied to them
How can a car be adapted for high acceleration?
If you are designing a car for high acceleration, the equation F = ma tells you that the car should have a low mass and the engine must provide a high accelerating force You must also consider the force to stop the car; when a moving object is stopped, it decelerates If a large deceleration is needed then the force causing the deceleration must by large too. Usually a car is stopped by using the brakes in a controlled way so that the decelerating is not excessive In an accident, the car may collide with another vehicle causing rapid deceleration
What is the centre of gravity?
If you balance a ruler on your finger, the anti clockwise and clockwise moments are equal, but there are no downward forces acting in this situation other than the weight of the ruler itself Since the mass of the ruler is spread evenly throughout the length, it finds its balance at its centre point We say that the gravity of the ruler is at this point. The weight force of the ruler acts through the centre of gravity so if we support the ruler at this point there is no turning moment in any direction about the point, and it balances. The centre of gravity is sometimes called the centre of mass.
What is the conservation of momentum
In any system, momentum is always conserved provided that no external forces act on the system This means that when two objects collide the momentum before the collision = the momentum after the collision provided that no friction forces act on them The presence of friction means that the balls will eventually slow down and stop, thus ending up with no momentum Although the balls have lost momentum something else will inevitably have gained an equal amount of momentum As the balls are slowed by the friction of the snooker table they, in turn, cause a friction force to act on the table so the table gains some momentum However, the large mass of the table means that the momentum is unnoticeable
Person A pushes the door with a force of 200 N at a distance of 20 cm from the hinge. Person B opens the door by pulling the door handle which is 80 cm from the hinge. What is the minimum pulling force that person B must use to open the door
Moment from person A = 200 x 20 = 4000 Nm So the moment from person B must be larger to open the door 80 x f = 4000 4000 / 80 = f f = 50 N so the force used must be greater than 50 N
What is the equation for the momentum of a moving object?
Momentum (kg m/s) = mass (kg) x velocity (m/s) p = m x v
What is momentum?
Momentum is a quantity possessed by masses in motion It is a measure of how difficult it is to stop something that is moving It is a vector quantity since it can be described by magnitude and direction Momentum is measured in kg m/s provided that the mass is measured in kg and the velocity is measured in m/s The more mass and speed and object has, the more momentum it will have when moving
What are Newton's laws of motion?
Newton's First Law of Motion: A body will continue to move in a straight line at a steady speed unless a resultant (unbalanced) force acts upon it If the forces acting on an object are balanced, then a stationary object stays in one place, and a moving object continues to move in just the same way as it did before the force was applied Newton's Second Law of Motion: The acceleration of an object depends on its mass and the net force exerted on it The bigger the force acting on an object, the faster the object speeds up The greater the mass of an object the larger the force needed to make them accelerate at the same rate of a smaller object Newton's third law: For every action there is an equal and opposite reaction Action and reaction forces are not balanced forces like friction and thrust acting on a car might be because they act on different objects. For example the weight of the car would be acting on the ground and the reaction force would be acting on the wheels of the car
How can we model terminal velocity?
Objects have to accelerate to high speeds to reach terminal velocity in air Objects falling through liquids also experience a drag force which is larger than that in air making it much easier to demonstrate with This means that objects falling through liquids have much lower terminal velocity than objects falling through air, and can be used to model terminal velocity You can use a tall measuring cylinder filled with water and drop small glass balls into it Alternatively use a much thicker liquid like oil
How can you find the speed of a car driving down the road?
Police use a mobile speed camera to check that drivers are keeping to the speed limit. Speed guns use microprocessors to produce and instant reading of the speed of a moving vehicle. However, the speed of a car can also be found manually using a click wheel to measure the distance between two points and then a stopwatch to measure the time. taken for a car to travel that distance: 1. Measure 50m from a start point along the side of the road and get your experiment partner to stand at that point 2. Start a stopwatch when your partner signals that the car is passing the start point 3. Stop the stopwatch when the car passes you at the finish point If it takes the car 3.9 seconds, the equation would be: v = 50 / 3.9 v = 12.8 m/s
What is the difference between speed and velocity?
Some displacement-time graphs have a linear, negative slope It is a straight line so the object is still moving at a constant speed but the line is sloping down to the right rather than up to the right The gradient of such a line is negative because the distance that the object is from the starting point is now decreasing and the object is going back on its path towards the start "Displacement" means distance travelled in a particular direction from a specified point So if the object was originally traveling in a northerly direction, the negative gradient of the graph means that it is now traveling south Displacement is an example of a vector quantity because it has a magnitutde (size) and a specific direction Velocity is also a vector and is the speed in a particular direction if a car travels around a bend, its speed is constant but its velocity will be changing for as long as the direction that the car is traveling in is changing Speed on the other hand, is a scalar quantity meaning it has magnitude but no specified direction. Therefore, you can't technically have a negative distance time graph because distance travelled can't decrease as time moves forward. Distance travelled from the origin in the opposite direction can That is the difference between speed and velocity
What is acceleration?
Some examples at which speed changes are: 1. Planes accelerate to reach take off speed 2. In ice hockey, the puck decelerates very slowly as it slides across the ice 3. When you drop and egg it is forced to decelerate very rapidly when it hit the ground. Rapid deceleration can be destructive Acceleration is the rate at which objects change their velocity Acceleration is a vector quantity because it is described by magnitude and direction
What are springs and wires used for and how to they change shape?
Springs are coiled length of certain metals which can be stretched or compressed by applying a force to them They are used to absorb raised bumps in the road as suspension springs in cars or bikes. In beds and chairs they are used to make sleeping and sitting more comfortable. They are also used in door locks to hold them closed and to make doors close automatically Springs change length when a force acts on them and they return to their original length when the force is removed This is true up until a certain point. Past that point they don't spring back to their original length
How are cars designed to be safer?
Steep roads often have escape lanes filled with deep, soft sand. The soft sand slows heavy lorries that are out of control slowly by making time, t, for the lorry to stop longer This makes the force slowing the lorry smaller and the driver is less likely to suffer serious injury Cars are now designed with various safety features that increase the time over which a car's momentum changes in an accident The car has a rigid passenger cell or compartment with crumple zones in front and behind The crumple zones collapse during a collision and increase the time during which the car is decelerating This only works is the passengers are wearing seat belts so that the deceleration applies to their body too Without seatbelt, the passengers will continue moving forward until they come into contact with some part of the car or the passenger in front If they hit something that does not crumple they will be brought to rest in a. very short time which means a large deceleration and as a result a large force acting on them.
How do brakes allow the car to stop?
The "tread" of a tyre is the grooved pattern moulded into the rubber surface It is designed to keep the rubber surface in contact with the road by throwing water away from the tyre surface Brakes on cars and bicycles work by increasing the friction between the rotating wheels and the body of the vehicle The friction force between the tires and the road depends on: 1. The condition of the tires- if the tires have good tread, are properly inflated 2. The surface of the road- if the road is dry or icy 3. The weight of the vehicle Maximum friction is achieved when the road is dry and the tires are inflated and have good tread Minimum friction occurs if the road is wet or the tires are in bad condition the friction force will be smaller If the brakes on a car are applied too hard, the tires will. no grip the road surface and the car will skid out of control. Once the car is skidding the driver no longer has control and it will take longer to stop Skidding can be avoided by applying the brakes in the correct way so that the wheels don't lock. Most modern cars are fitted with an anti-braking system that senses when the car is about skid and releases the brakes for a very short time
What does the area under a velocity-time graph signify?
The area under a velocity- time graph shows the distance travelled If an object travels at a constant velocity of 5 m/s for 10s, a simple calculation shows that the object has travelled 50 m since 5 x 10 gives the area underneath the line This method works for a graph with a straight horizontal line - no acceleration However for linear graphs where the gradient is not zero, the area of a triangle equation should be used: area of a triangle = 1/2 base x height
How can you find the centre of gravity of a sheet of card?
The centre will be located where the axes of symmetry cross
How does the conservation of momentum principle apply to explosions?
The conservation of momentum principle can be applied to explosions An explosion involves a release of energy causing things to fly apart The momentum before and after the explosion remains unchanged though there will be a huge increase in movement energy You might think that rockets take off because the rocket motor is pushing against the ground but rockets work in space where there is nothing to push against Rocket motors use the principle of conservation of momentum to propel the space craft through space. They produce a continuous, controlled explosion that forces large amounts of fast moving gases (produced by the fuel burning) out the back of the rocket The spacecraft gains an equal amount of momentum in the opposite direction to that of the moving exhaust gases
Why is it important for the clockwise and anti clockwise moments of a crane to be balanced?
The load arm of a crane of a crane is long so that the crane can reach across a construction site and move loads backwards and forwards along the length of the arm The weight of the long load arm and the load must be counterbalanced by the large concrete blocks at the end of the short arm that projects out behind the crane controller's cabin The counterbalance weights must be large because they are positioned closer to the pivot point where the crane tower supports the crosspiece of the crane Without careful balance, the turning forces on the support tower could cause the crane to bend and collapse
What forces act on a car when a man starts pushing it?
The man applies a pushing force on the car. He struggles to make the car move due to the forces acting on the car to stop it moving This force is friction between the moving parts in the car engine, gears, wheel axles and so on. This force opposes the motion that the man is trying to achieve. However, when the car engine is doing the work to move the car, the friction between the tires and the road surface is vital since on an icy road even powerful cars may not move forward because there is not enough friction between the types and the ice Another force acting on the car is gravitational force or weight. If the car were to be pushed over the edge of a cliff, the effect of the gravitational force would cause the car to fall downwards. In this scenario, the road seems to be stopping the car from being dragged into the earth. This force acts in an upward direction on the car and is called the normal reaction force (the word normal means acting at 90 degrees to the road's surface) In summary: 1. Friction 2. Thrust 3. Weight 4. Reaction force
How is the centre of gravity related to stability?
The position of the centre of gravity of an object will affect its stability. A stable object is one that is difficult to push over. When pushed and then released it will tend to return to its previous position A bottle with a low centre of gravity and a broad base is stable and difficult to knock over. It is stable because when knocked its low centre of gravity and wide base result via turning moment that tries to pull it back to its original position A bottle with a higher centre of gravity and a narrow base is more easy to knock over because only a small displacement is needed to knock it over
What is the stopping distance?
The stopping distance = the braking distance + the thinking distance
How does momentum change during a collision?
The total momentum of object that collide remains the same: Momentum before collision = momentum after collision mass a x velocity a = mass b x velocity b This can be used to work out what happens to objects that collide when they are moving along the same straight line We can express this in terms of momentum change: Force x time (impulse) = increase in momentum This simply says that a bigger force applied to an object for a longer time will result in a greater change in the momentum of the object a) A ball is rolling towards a stationary ball b) During the impact each ball exerts a force on the other - equal in size and opposite in direction c) After the collision, both balls move in the same direction. An increase in momentum in ball B is balanced by a decrease in momentum in ball A so the total momentum is the same before and after the collision - momentum is conserved During the time the two balls are in contact each exerts a force on the other Newton's third law states that the forces act in opposite directions for the same amount of time which means that the impulse is the same size but in opposite directions
What is the moment of a force?
The turning effect of a force about a hinge, pivot or fulcrum is called a moment moment of a force (Nm) = force, (N) x perpendicular distance from pivot (m) Moment = F x d The moment of a force is measured in newton meters (Nm) because force is measured in newtons and the distance to the pivot is in meters We need to be precise about distance when we are calculating the moment of a force. The distance is measured perpendicular to the line of action to the pivot For a force to have the biggest turning effect it should be applied perpendicular to the lever (at a 90 degree angle) If the force is applied along a line passing through the pivot there will be no turning effect
What are the units of force?
The unit used to describe force is newtons (N) and is named after Sir Isaac Newton A force of one newton will make a mass of one kilogram accelerate at one metre per second squared An apple weighs about 1 N and a bag of sugar weights about 10 N
What is weight?
The weight of an object is the force that acts on it because of gravity The weight of an object depends on its mass and the strength of gravity The gravitational field strength (g) is the force that acts on each kilogram of mass We can work out the weight of an object using this equation: weight (N) = mass (kg) x gravitational field strength (N/kg) W = m x g Near and on the Earth's surface the gravitational field strength is approximately 9.8 N/kg but we often use 10 N/kg to make calculations easier The gravitational field strength on the moon is about 1.6 N/kg so an object taken from the Earth to the moon will have less weight even though it has the same mass
What are balanced and unbalanced forces?
Unbalanced forces on an object cause it to change the way it's moving Balanced force on an object don't change the way it's moving Tug of war: In a tug of war contest two teams are pulling on the rope in opposite directions. For much of the time the rope doesn't move because the two forces are balanced. This means that the forces are the same size and acting in opposite directions along the line of the rope. There is no unbalanced force in one direction or the other. When the forces acting on something are balanced, the object doesn't change the way it's moving. In this case, the rope is stationary so it remains stationary. Eventually, one of the teams will get tired and its pull will be smaller than that of the other team. When the forces acting on the rope are unbalanced, the rope will start to move in the direction of the greater force. There will be an unbalanced force in that direction. The rope was stationary and the unbalanced forces acting on it are causing it to accelerate Cars: Sports cars are designed to have an enormous acceleration from rest. As soon as it starts to move the forces that oppose motion (friction and drag) must be overcome. The thrust of the engine is, to start with, much greater than the friction and drag forces. This means that the forces acting on the car in the horizontal direction are unbalanced and the result is a change in the way that the car moves - it accelerates Once the friction forces balance the thrust the car no longer accelerates, it moves at a steady speed
What are velocity time graphs?
Using Galileo's experiment, if you have the distance between the bells and the time taken between them you can calculate the velocity: velocity = distance moved / time Let's say that the result of this is the velocity over a 0.5 second interval; we should plot it on the graph at the middle of the interval which would be 0.25 seconds Once you have these results, you can plot a velocity time graph of velocity on the y axis against time on the x axis Using the equation as as shown above only works for objects with uniform or constant acceleration so the graph will have a straight line The steeper the gradient, the greater the acceleration The acceleration can be found by calculating the gradient of the graph: 1. Draw a big triangle - the length of the base is the time and the height is the velocity 2. Divide the height by the length Here are some examples of different graphs and how they are affected by acceleration: a) Shallow gradient - low acceleration b) Steep gradient - high acceleration c) Horizontal - no acceleration or a constant velocity d) Negative gradient - negative acceleration (deceleration)
What is resultant force?
Using the example of the man pushing the car again, he is pushing in one direction and friction is opposing his motion. These two forces act along the same line but in the opposite direction which means that one is negative (because it acts in the opposite direction to the other) If they are equal in size, the resultant force will be zero and the fear will not move In this case, the forces are balanced If the man get someone to help him push the car, the forward force is bigger. Since both of the forces pushing the car are acting in the same direction, you can find the total forward force by adding them together. If both people are pushing with a force of 100 N then: 300 N + 300 N = 600 N Now, we can find the resultant force on the car and discover which way the car will move in. Since force is a vector quantity, it is important that we think about the directions in which the forces are acting. We can do this by deciding which direction is the positive direction. In this case, we can decide that the force from the people is positive and the force from the friction is negative: If the friction is -300 N 600 - 300 = 300 It will be an unbalanced force since there is a resultant force in the positive direction and as a result the car will move forwards.
What is the unit for acceleration?
Velocity is a vector quantity just like acceleration and is measured in m/s Acceleration, the rate of increase in velocity with time, is therefore measured in m/s/s so it's written as m/s2 Other units such as cm/s2 can also be used
What do distance time graphs show us?
Vertical axis - distance travelled Horizontal axis - time If the graph is linear, the speed is constant or steady therefore it is the same value throughout the whole graph However, if the line isn't linear, the speed is constantly changing so to find the speed at a certain point we need to draw a tangent to the curve and find the gradient of the tangent The gradient tells us the speed of the car (y / x) 3. Horizontal line - the distance is not changing with time so the speed is zero 4. a) Steeper - greater speed b) Flatter - lower speed 5. Line getting steeper - gradient is getting bigger so the object is accelerating (speeding up) 6. Line getting gentler - gradient is getting smaller so the object is decelerating (slowing down)
Explain Galileo's method for measuring acceleration?
When a ball is rolled down a slop it is clear that its speed increases as it rolls (it accelerates) Galileo was interested in how and why objects speed up and how the distance travelled by a ball depends on the time it has been rolling: 1. He set up a slope with a series of bells hanging above it at equal heights 2. The ball rolling down the slope ill strike the series of bells as it rolls 3. By adjusting the distances of the bells from each other, it is possible to make the bells ring at regular intervals as the ball passes (Galileo used the pulse of his heart to measure this) 4. This will result in the distances between the bells increasing further down the slope, showing that the ball is traveling faster as time passes on 5. You should also notice that the distance travelled increases in a predictable way. This is known as uniform acceleration although most acceleration is actually non-uniform
What is the thinking distance?
When a driver sees and object blocking the way ahead, it takes time for him or her to respond to the new situation before taking any action This is called the reaction time and depends on the person driving the car It also depends on whether: 1. The driver is tired 2. Under the influence of alcohol or other drugs that slow reactions 3. Poor visibility due to fog or sight impairment 4. How fast the car is going because the faster the car the further it will travel during the thinking time
How do parachutes work?
When a skydiver jumps from a plane they will accelerate for a time and eventually reach terminal velocity When they open their parachute this will cause a sudden increase in the drag force. At this velocity the drag force of the parachute is greater than the weight of the skydiver so the unbalanced force acting on the parachutist acts upwards and for a while will decelerate As they slow down the size of the drag force decreases and a new terminal velocity is reached The velocity depends on the design on the parachute but is must be low enough to allow the parachutist to land safely On the graph, the first plateau represents free fall terminal velocity and the second represents terminal velocity with an open parachute The parachute opens at the point
What is the relationship between momentum and acceleration?
When an unbalanced force acts on an object it causes a change in the momentum of the object in the direction of the unbalanced force The rate of change of momentum of an object is proportional to the force applied to it This means if you double the force acting on an object its momentum will change twice as quickly The thrust of the rocket motor makes the velocity and, therefore, the momentum of the shuttle increase a) The rocket is traveling at initial velocity, u b) A thrust force acts on the rocket causing an unbalanced force and leading to acceleration c) The final velocity, v is reached when the forces balance out once more initial momentum of an object = mu final momentum of an object = mv Increase in momentum = mv-mu So rate of increase of momentum = (mv - mu) / t force, F = change in momentum (mv-mu) / time taken, t F = mv-mu / t This equation can actually be rearrange to get the other equation for force: F = ma 1. F = mv-mu / t = m(v - u) / t since (v - u) / t = a then F = ma This rearrangement is possible if we assume that the mass of the object involved is constant which will not always be the case in real situations. For example, when a space shuttle is launched the mass of the rocket changes continuously as fuel is burned and rocket stages are jettisoned. Rocket scientists also have to include air resistance in their calculations
What occurs when there is low friction?
When there is very low friction, an object can be given a small push and will continue to move at a constant speed even when the force is no longer acting on it A similar effect is seen in space where objects keep moving in a straight line once they are set in motion. This occurs because the objects are weightless and the force of air resistance acting on them is very small. Although the objects can be described as "weightless" because they don't appear to have any gravitational force acting upon them. However, Earth's gravity is still acting upon them. For example, objects in a space craft can be thought of as falling around the Earth. Since the spacecraft in orbit is also falling around the Earth at the same rate, they don't appear to fall inside of it.
What is the braking distance?
With ABS braking, in an emergency you break as hard as you can. This means that the braking force will be a maximum and we can work out the deceleration using: F = ma rearranged to give a = F/m Vehicles with large masses, like lorries, will have smaller rates of deceleration for a given braking force (they will travel further while braking) The distance travelled can be found by looking at the area underneath the line of a velocity-time graph In two graphs, one has a steeper gradient and therefore a higher deceleration and the other has a shallower gradient and therefore a lower deceleration They are both braking from the same velocity so car A is braking harder than car B and comes to rest in a shorter time Car B travels further before stopping as seen by the large area under the graph The maximum rate of deceleration depends on how hard you can brake without skidding- in poor conditions the braking force will be lower If there are two cars and one is braking from a lower velocity than the other but they decelerate at the same rate, the car braking at a higher velocity will take longer to stop and will travel further while stopping Braking takes longer if: 1. Tires are in poor condition 2. The road is wet or slippery 3. The vehicle has a large mass
What are some alternative methods for the experiment above?
You could investigate the motion of moving objects using photographic methods: 1. Carrying out the experiment in a darkened room using a stroboscope to light up the object with a piece of reflective tape on it. This usually works for motors or objects that move in a circular fashion. To find the speed, you can change the frequency setting on the stroboscope until you get the lowest setting at which the reflective tape is still. At this stage the frequency (measured in revolutions per minute) will equal the number of times one full cycle can occur per minute 2. Using a video camera and noting how far the object has travelled between each frame 3. Using an electronically operated stop watch and electronic timing gates. This removes timing errors produced by human reaction time. To do this, attach a piece of card to the object and the timing gate will measure how long it takes for that card to pass it. Then, using the length of the card as the value for distance and the measurement on the stop watch for time, you can calculate the average speed of the object as it passes through the timing gate
An object hits the ground traveling at 40 m/s. It is brought to rest in 0.02 s. What is it's acceleration?
a = ( v - u ) / t a = (0 - 40) / 0.02 a = -2000 m/s squared
A stone accelerates from rest uniformly at 10 m/s squared when it is dropped down a deep well. It hits the water at the bottom of the well after 5s. Calculate how fast it's traveling when it hits the water.
a = (v-u) / t 10 = v / 5 10 x 5 = v 50 m/s
a ) A car traveling at 20 m/s collides with a stationary lorry and stops completely in just 0.02 s. Calculate the deceleration of the car. b) A person of mass 50 kg in the car experiences the same deceleration when she comes into contact with a hard surface in the car. This could be the dashboard or the windscreen. Calculate the force that the person experiences.
a = (v-u) / t a = (0-20) / 0.02 a = -20 / 0.02 a = -1000 m/s squared F = 1000 x 50 F = 50,000 N
A GPS shows two points on a journey. The second point is 3 km north-west of the first. a) A walker takes 45 minutes to travel from the first point to the second. Calculate the average velocity of the walker. b) Explain why the average speed of the walker must be greater than this
a) 3000/2700 = 1.1 m/s or = 4 km/h b) Because the equation for velocity uses displacement from a point rather than distance travelled This means that whilst the walker followed curving roads the displacement is linear So that walker's average speed calculated using distance would be greater than the velocity calculated using displacement
The first stage of the type of rocket used in the Moon missions provides and unbalanced upward force of 30 MN and burns for 2.5 minutes. a) Calculate the increase in the rocket's momentum that results b) If the rocket has a mass of 3000 tonnes, what is the velocity of the rocket after the first stage has completed its "burn"?
a) F = (mv-mu) / t 30 x 1,000,000 = 30,000,000 N 30,000,000 = (mv-mu) / 190 30,000,000 x 150 = mv - mu mv-mu = 4,500,000,000 kg m/s b) F = m (v-u / t) 30,000,000 N = 3,000,000 kg (v-u/150) 10 = v-u/150 1500 m/s = v-u Or you could divide you answer to part "a" by mass to convert mv to v
An astronaut in space has a mass of 140 kg How much will the astronaut weigh on: a) Earth b) Mars (gravitational field strength is a third of that on Earth)
a) Weight = 140 x 10 Weight = 1400 N/kg b) Weight = 140 x 3.34 Weight = 468 N
A car is traveling at 20 m/s. It accelerates steadily for 5s after which time it is traveling at 30 m/s. Can you calculate its acceleration?
acceleration = final velocity - initial velocity / time a = ( 30 - 20 ) / 5 a = 2 m/s squared
What is the calculation for average speed?
average speed (m/s) = distance moved (m) / time taken (s) v = s / t The average speed is the total distance travelled divided by the time taken for the journey To use the triangle to find the equation for speed for a different subject, cover up the part of the triangle that you want to find. For example 't' Once you cover 't' the triangle will read s/v So the equation for time would be: time = distance / speed
What is the formula for velocity?
average velocity = increase in displacement / time taken
A cylinder containing a vaccine is dropped from a helicopter hovering at a height of 200m above the ground. The acceleration due to gravity is 10 m/s^2. Calculate the speed at which the cylinder will hit the ground
v^2 = u^2 + 2as v^2 = 0^2 + 2 x 10 x 200 v^2 = 0 +4000 v^2 = 4000 m^2/s^2 v = 63.25 m/s