Unit 1.1: Mechanics
What is the principal of conservation of momentum?
*Assuming NO EXTERNAL FORCES* act, momentum is always CONSERVED. This means the *total momentum of two objects before they collide* *= the total momentum after the collision*
What is kinetic energy and its formula
*Kinetic energy* is the energy of anything due to its *motion*, which you work out from: Ek = 1/2 mv^2 (don't forget the squared)
What is a scalar and a vector quantity
*Scalar quantity* - only has *size* but not direction e.g. mass, time, energy temperature, length, speed, Ampere *Vector quantity* - has magnitude *(size)* and *direction* e.g. displacement, force, velocity, acceleration, momentum -
What is speed, velocity and acceleration
*Speed* - How *fast* something is moving, regardless of direction/rate of change of distance *Velocity* - The rate of change of an object's displacement (its *speed in a given direction*). *Acceleration* - The rate of change of velocity - acceleration could mean a change in speed or direction or both
What are the features of a displacement time graph (3)
- A displacement-time graph can have a *negative* portion in the *y axis* if *displacement is backwards* - A *horizontal line* means the object is *stationary* - The *gradient of a displacement* time graph give *velocity* (v = change in displacement/time)
What does changes in acceleration for a displacement time graph look like?
- A graph of displacement against time for an *uniformly accelerating object* always *produces a curve*. The *rate of change of the gradient* will be *constant* - The *higher* the *acceleration*, the *more steep the rate of change* e.g. Plot a displacement-time graph for a lion who accelerates constantly from rest at 2 ms-2 for 5 seconds - If an object is *decelerating*, the *displacement would increase at a decreasing rate* (gradient decreases)
What are the features of a velocity time (v-t) graph
- The *gradient* of a v-t graph is *acceleration*, the steeper the gradient, the higher acceleration *(because y = mx +c == v = u + at)* - *Displacement = area under graph* (Areas under any *negative parts of the graph* count as *negative areas,* as they show the object moving back to its start point.)
How is Drag affected in fluids
- The force of drag will depend on the *viscosity* of the fluid. - Drag *increases* as *speed increases* - The *larger the area* of the object, the *larger the drag force*
How do you find the center of gravity of an irregular object
1) *Hang* the object *freely from a point* (e.g. one corner). 2) *Draw a vertical line downwards* from the *point of suspension* — use a *plumb bob* to get your line exactly vertical. 3) *Hang* the object from a *different point*. 4) Draw *another vertical line down*. 5) The centre of gravity is where the *two lines cross*. You can also find the center of gravity using the *principle of moments (ACM = CM)*
How do you find the projectile motion of a projectile moving at an angle
1) *Resolve* the initial *velocity* into *horizontal and vertical components*: horizontal velocity = *vh = v cosθ* vertical velocity = *vv = v sinθ* 2) Often you'll use the vertical component to work out *how long it's in the air* and/or *how high it goes*, and the *horizontal component* to work out *how far it goes while it's in the air.*
CORE PRACTICAL 1: Determine the acceleration of a freely-falling object Procedure
1) *Set up the equipment* shown in the diagram on the right. 2) *Measure the height h* from the bottom of the ball *bearing to the trapdoor.* 3) *Flick the switch to simultaneously start the timer and disconnect the electromagnet*, *releasing the ball bearing.* 4) The *ball bearing falls*, *knocking the trapdoor down* and *breaking the circuit* — which *stops the timer.* *Record the time t* shown on the timer. 5) *Repeat* this experiment *three times* and *average* the time taken to fall from this height. *Repeat* this experiment but drop the ball from *several different heights*. 6) You can then use these results to find g using a graph
Describe how a sky diver reaches terminal velocity
1) A skydiver leaves a plane and will *accelerate* due to his *weight.* As he *accelerates*, *air resistance increases* so his *rate of acceleration decreases* until the *air resistance equals his weight* 2) When *upwards* air resistance = weight, there is no resultant force, so constant velocity or *terminal velocity* or *no acceleration* 3) Before reaching the ground he will *open his parachute,* which immediately *increases the air resistance* so it is now *bigger than his weight.* 4) This *slows him down* until his *speed has dropped* enough for the *air resistance to be equal to his weight* again. This new *lower terminal velocity* is small enough for him to *land safely*.
How can you use the principle of moments to calculate the center of gravity of a broom
1) All the weight of an object acts through its center of gravity, so: 2) If you are trying to balance a broomstick on a pivot. If the *center of gravity is to one side of the pivot* then there will be a *clockwise moment* due to the *weight of the broomstick* acting at a *distance from the pivot*. There is *no anticlockwise moment,* so the *broomstick will rotate clockwise* (fall off the pivot). 3) However, if the *center of gravity is directly above the pivot,* then there are *no clockwise or anticlockwise moments* and so the broomstick is in *equilibrium.*
Describe the motion of the cyclist using the displacement-time graph
1) At first there is *constant velocity* 2) Then there is *acceleration* 3) Then there is a *higher constant velocity*
Example 2: A van is accelerating north, with a resultant force of 510 N. A wind begins to blow on a bearing of 150º. It exerts a force of 200 N (to 2 s.f.) on the van. What is the new resultant force acting on the van?
1) Draw a *scale diagram* of the 2 vectors e.g. *1cm = 100N* 2) Measure the angle of 150º and the sides where 200N = 2cm and 510N = 5.1N 3) Draw the resultant force between these 2 forces and measure the length of the force 4) *Convert the length in cm to N using your scale and find the direction of the force (350N, at 17º - 2s.f.)*
Example: Projectile motion at an angle Q) An athlete throws a javelin from a *height of 1.8 m* with a velocity of 21 ms-1 at an upward angle of 45° to the ground. How far is the javelin thrown? Assume the javelin acts as a particle, the ground is horizontal and there is no air resistance. (THIS IS A HARD QUESTION)
1) Draw a quick sketch of the question --> 2) vertical velocity, *uv* = *21 x sin 45° = 14.85 m/s* horizontal velocity, *uh* = 21 x cos 45° = 14.85 m/s 3) Then find *how long it's in the air for* — start by finding *vv* . The *javelin starts from a height of 1.8 m* and *finishes at ground level*, so its *final vertical distance sV = -1.8 m:* v^2 = u^2 + 2as == v^2 = u^2 + 2gs v = √ 14.85^2 + 2 x *(-9.81)* x (-1.8) <-- *DON'T FORGET, g is NEGATIVE* v = - 15.995 m/s *( -ve bc VELOCITY DOWNWARDS)* s = (u + v)t/2 so, *t = 2s/(u + v)* t = 2(-1.8) / (14.85 + - 15.995) t = *3.1144 s* 4) Finally, as *ah = 0*, you can use *speed = distance / time* to work out *how far it travels horizontally* in this time. The horizontal velocity is just uh,so: *sh = uht* = 14.84... × 3.144... = 46.68... = 47 m (to 2 s.f.) well ... that was hard. Get used to it.
How do you find the resultant force using the parallelogram rule
1) Draw the 2 vectors tip to top using a scale e.g. 1cm = 100N 2) Draw parallel lines opposite these vectors with the same length and direction 3) The resultant force is the *scale length of the diagonal between the vectors* and the angle can be found with a protractor
What is a free body force diagram?
1) FBDs show *all the forces that act on a single body*, but *not* the *forces it exerts* on the rest of the world. 2) Remember forces are *vector *quantities and so the arrow labels should show the *size and direction*. 3) If a body is in *equilibrium* (i.e. not accelerating) the *forces acting on it will be balanced.*
How do you show increasing and decreasing acceleration (non uniform) on a v-t graph
1) Increasing acceleration would give a curve with an increasing gradient 2) Decreasing acceleration would give a curve with an decreasing gradient
How do you find the resultant (sum) vector from 2 forces perpendicular to each other or not perpendicular
1) Start by *drawing a diagram.* Draw the vectors *'tip to tail'*. If you're doing a vector subtraction, draw the vector you're subtracting with the same magnitude but pointing in the opposite direction 2) If the vectors are at *right angles* to each other, then you can use *Pythagoras to find the size and TIRG to find the ANGLE* of the resultant force. 3) If the vectors aren't at *right angles*, you may need to draw a *scale diagram*.
How do you find the center of gravity of a regular object
1) To find the centre of gravity for a regular object you can just use *symmetry.* 2) The centre of gravity of any regular shape is at its *centre* — where the *lines of symmetry will cross*. 3) The centre of gravity is *halfway through the thickness* of the object at the point the lines meet.
CORE PRACTICAL 1: Determine the acceleration of a freely-falling object Graph
1) Use your *data* from the experiment to *plot a graph of height* (s) *against the time* it takes the ball to fall, *SQUARED (t^2).* Then draw a *line of best fit* 2) You know that with *constant acceleration, s = ut + ½at^2*. If you drop the ball, *initial speed u = 0,* so s = ½at2. 3) Rearranging this gives *½a = t s 2 , or ½g = t s 2 *(remember the acceleration is all due to gravity) 4) So the *gradient of the line of best fit, (s/t^2) , is equal to ½g* 5)As you *know g (9.8 ms-2 to 2 s.f.)* you can *calculate the percentage difference* between *your value of g and the true value*, and use this to *evaluate the accuracy* of your results.
How can projectile motion be investigated using a video camera
1) You can *plot the course taken by an object* by recording its *position in each frame*. 2) If you know the *frame rate*, and your *video includes a meter ruler or grid lines* that you can use as a *scale*, you can *calculate the velocity* of the *projectile between different points* in its motion, by looking at *how far it travels between frames.*
Example: Power A light bulb transfers 230 kJ of electrical energy into light and heat in one hour. Calculate the power of the bulb.
230 kJ = 230,000 J 1 hr = 3,600 s P = E/t P = 230,000/3600 P = 63.89 = 64 W (2 s.f.)
What are the features of an acceleration-time graph (4)
An acceleration-time graph shows how an *object's acceleration changes over time*. 1) The *height* of the graph gives the object's *acceleration at that time*. If the *height is negative*, the object is *decelerating* 2) The *area under the graph* gives the object's *change in velocity.* 3) *If a = 0*, then the object is moving with *constant velocity. (either stationary or constant velocity)*
How can an air track be used to investigate momentum
An air track is a track with a series of small *holes* along its surfaces. *Air is blown through the holes.* This *reduces friction* between the track and the trolleys. *Momentum is only conserved if NO EXTERNAL FORCES act,* so air tracks are *useful for studying conservation of momentum* as you can assume there is *NO FRICTION*
How can an air track and light gates be used to investigate momentum
As there are *no external forces (friction)* on an air track, *momentum can be investigated* 1) *Two trolleys are pushed towards* each other on an air track, so that they *collide between the light gates.* The *light gates measure the speed of each trolley* as they pass through them. If the *speed of each trolley is measured before and after the collision*, the *initial and final momentum* of each trolley can be *calculated using p = mv.*
What is the average speed and instantaneous speed
Average speed is total distance covered divided by time, *instantaneous speed is speed at any instant.*
Why do all energy transfers involve losses
Because *no device is 100% efficient,* there will always be energy losses e.g. in the form of heat due to friction e.g. a computer gets hot (loses chemical energy to thermal energy)
Example: Adding the Components Back Together to get the Resultant Force Two dung beetles roll a dung ball along the ground at a constant velocity. Beetle A applies a force of 0.50 N northwards while beetle B exerts a force of 0.20 N eastwards. What is the resultant force on the dung ball? (remember *size and direction)*
By Pythagoras, R2 = 0.50^2 + 0.20^2 = 0.29 R = .0 29 = 0.538... = *0.54 N* (to 2 s.f.) θ = tan-1 (0.20/0.50) θ = 21.8°... = 22° (to 2 s.f.) *So the resultant force is 0.54 N at an angle of 22° to the vertical (i.e. a bearing of 022°).*
What are the equations for efficiency
Efficiency = useful *energy*output / total *energy* input OR Efficiency = useful *power* output / total *power* input Usually you multiply by 100 to find efficiency as a %
What is the principle of conservation of energy
Energy *cannot be created or destroyed.* Energy can be *transferred* from one form to another but the total amount of energy in a closed system will not change.
Example: Force = change in momentum/time A snooker ball that is initially at rest is hit with a cue. The cue is in contact with the ball for 0.0040 s and the speed of the ball immediately after being hit is 0.80 ms-1. The mass of the snooker ball is 0.16 kg. Calculate the average force exerted on the snooker ball by the cue.
F = (0.16x0.8)-(0.16x0)/0.004 F = 32N
What is resolving a force
Finding perpendicular components that have a resultant force that is equal to the force *(by trigonometry)* e.g. *Working backwards and finding the vertical Force A and horizontal Force B from the resultant force*
Example 1: Jemima goes for a walk. She walks 3.0 m north and 4.0 m east. She has walked 7.0 m but she isn't 7.0 m from her starting point. Find the magnitude and DIRECTION of her displacement
First, draw the vectors *tip-to-tail*. Then draw a line from the *tail* of the *first vector* to the *tip* of the* last vector* to give the resultant Because the vectors are at right angles, you get the magnitude of the resultant using *Pythagoras*: R^2 = 3.0^2 + 4.0^2 = 25.0 So R = 5.0 m
What is the principle of MOMENTS
For a body to be in *equilibrium*, the *sum of the clockwise moments* about any point *equals the sum of the anticlockwise moments* about the same point
What is friction and drag
Friction - a force that opposes motion (acts opposite in direction to motion) *Drag - friction in fluids* (gases and liquids)
What is gravitational potential energy and its formula
Gravitational potential energy is the *energy something gains if you lift it up*. The equation for the change in gravitational potential energy close to the *Earth's surface* is: ∆E grav = mg∆h where g = 9.81 ms-2 height is in meters and m is in kg
Example: resolving a force A tree trunk is pulled along the ground by an elephant exerting a force of 1200 N at an angle of 25° to the horizontal. Calculate the components of this force in the horizontal and vertical directions.
Horizontal force: 1200 × cos 25° = 1087.5... = 1100 N (to 2 s.f.) Vertical force: 1200 × sin 25° = 507.1... = 510 N (to 2 s.f.)
How does the conservation of momentum relate to Newton's 3rd law
If *object A collides with object B* and *exerts a force F* on B for a *time Dt*, Newton's 3rd law says that *object B will also exert a force -F on A* for a *time Dt*. The *change in A's momentum is equal to -FDt*, and the *change in B's momentum is FDt,* so the *overall change in momentum is (-FDt) + FDt = 0*. So momentum is conserved
What is Newton's 3rd law
If an object A exerts a *FORCE on object B*, then object B exerts *AN EQUAL BUT OPPOSITE FORCE on object A* e.g. If you push against a wall, the wall will push back against you, just as hard. As soon as you stop pushing, so does the wall. Amazing...
How can you investigate projectile motion using *STROBE PHOTOGRAPHY*
In *strobe photography*, a *camera* is set to take a *LONG EXPOSURE*. While the camera is taking the photo, a *strobe light flashes repeatedly* and the projectile is released. The strobe light *lights up the projectile* at *regular intervals*. This means that the *projectile appears multiple times* in the *SAME PHOTO*, in a *different position each time*. Again, if you've got a *reference object* in the photo (for example, you might throw an object in front of a screen with a *grid drawn on it*), you can *calculate how far the object travels between flashes* of the strobe, and use the *time between flashes* to *calculate the velocity* of the *projectile between the flashes.*
What are the 4 main equations that you use to solve problems involving *uniform acceleration* (SUVAT equations)? (note, you don't have to memorize any equations for A-Level Physics, they are all provided in the formula booklet)
Its worth memorizing these equations v = final velocity u = initial velocity s = displacement t = time taken
How is MOMENT calculated
Moment = Force x perpendicular distance from pivot moment (Nm) = Fx
What is Newton's first law?
Newton's 1st law of motion states that the *velocity/acceleration (a=0)* of an object will *not change* unless a *resultant force acts on it.* e.g. A object falling at *terminal velocity* will not accelerate *(a=0)* because its *weight and drag forces are balanced*
What does Newton's 2nd law state about force and momentum (equation)
Newton's 2nd Law Says *That Force is the Rate of Change in Momentum*
What are the conditions for Newton's 3rd law
Newton's 3rd law applies in all situations and to all types of force. But the *pairs of forces* are always the *same type*, e.g. *both gravitational* or *both electrical*, and they *act along the same line.*
What objects are more stable
Objects with a large base area or low center of gravity (less likely to topple over)
What are the equations for power (2)
Power (W) = Work (J)/Time (s) P = W/t Power (W) = Energy transferred (J) / Time (s) P = E/t
What are projectiles and what path do they follow?
Projectiles are objects given an initial velocity and then left *freely to move under gravity*
What is weight and its equation
The *force on an object due to gravity* is called its weight W = mg where g = 9.81 Nkg-1
Example: Q) A space probe free-falls towards the surface of a planet. The graph on the right shows the velocity of the probe as it falls. a) The planet does not have an atmosphere. Explain how you can tell this from the graph. [2 marks]
The *velocity increases at a steady rate*, which means the *acceleration is constant* [1 mark]. Constant acceleration means there must be *no atmospheric resistance* (atmospheric resistance would increase with velocity, leading to a decrease in acceleration). So there must be *no atmosphere* [1 mark].
What is a moment
The turning effect of a force
Example: Horizontal projectile motion 2 Q) Jane fires a scale model of a TV talent show presenter horizontally from *1.5 m above the ground* with a *velocity of 100 ms-1* (to 2 s.f.). b) *How far does it travel horizontally?* Assume the model acts as a particle, the ground is horizontal and there's no air resistance
Then do the horizontal motion: 1) The *horizontal motion ISN'T affected by GRAVITY* or any other force, so it *moves at a CONSTANT SPEED*. That means you can just use good old *speed = distance / time*. 2) Now v = 100 ms-1, t = 0.553... s and a = 0. You need to find s. *3) s = vt = 100 × 0.553... = 55 m (to 2 s.f.)*
Example: Horizontal projectile motion 1 Q) Jane fires a scale model of a TV talent show presenter horizontally from *1.5 m above the ground* with a *velocity of 100 ms-1* (to 2 s.f.). a) How long does it take to *hit the ground*?* Assume the model acts as a particle, the ground is horizontal and there's no air resistance
Think about *vertical motion first: * 1) It's *constant acceleration* under *gravity*... 2) You know *u = 0* (no VERTICAL velocity at first), *s = -1.5 m and a = g = -9.81 ms-2*. You need to *find t*. *3) Use s = 1/2gt^2 t = √(2s/g) = √(2(-1.5)/(-9.81)) t = = 0.553... s. So the model hits the ground after 0.55 (to 2 s.f.) seconds*
How do you find the instantaneous velocity from a displacement time graph at any time? (if the gradient isn't constant)
To find the instantaneous velocity at a certain point you need to draw a *tangent* to the curve at that point and find its *gradient*
Example: Conservation of momentum (collisions) Q) A skater of mass 75 kg and velocity 4.0 ms-1 collides with a stationary skater of mass 50 kg (to 2 s.f.). The two skaters join together and move off in the same direction. Calculate their velocity after impact
Total momentum before = (75 x 4) + (50 x 0) = 300kg m/s Total momentum after = (75+50)v = 300 v = 300/125 = 2.4 m/s
Example: conservation of momentum (explosions) A bullet of mass 0.0050 kg is shot from a rifle at a speed of 200 ms-1 (to 2 s.f.). The rifle has a mass of 4.0 kg. Calculate the velocity at which the rifle recoils
Total momentum before = 0 kg m/s Momentum after = 0.005x200 = (1 kg m/s - 4v) = 0 -v = 1/4 v = - 0.25 m/s (momentum is conserved)
What is vector notation
Vectors are usually written in *bold* or have an *arrow on top*
Example: moment question Q) A diver of mass 60 kg stands on the end of a diving board 2.0 m from the pivot point. Calculate the downward force exerted on the board by the retaining spring 30 cm from the pivot
W = mg W = 60 x 9.81 = 588.6 0.3F = 588.6N x 2 F = 1177.2/0.3 F = 3924 = 4000N (1 s.f.)
What is work done and its formula (2)
Work is the *energy transferred* from *one form to another* by a *force* that causes a *movement* of some sort. It's measured in joules (J) e.g. lifting a book is *work done against gravity* ∆work done (N) = force causing motion (N) × ∆distance moved (m), or *∆W = F∆s* Work also = the energy transferred
How do you find the area under a curved graph (v-t or a-t graph)
You have to estimate the area by: - Split the area under the curve up into *trapeziums and a triangle.* - Calculate the sum of the areas of all the trapeziums and triangles - Always *check the axes* to make sure your units are correct
How do you calculate work if the direction of movement is different to to the direction of the force
You will need to consider the *horizontal and vertical components* of the force - If the force is at an angle to the horizon but the object is *only moving horizontally, (the vertical force is not causing any motion)* so, the *horizontal force is causing the motion* — so to calculate the work done, this is the *only force you need to consider*.
Example: Gravitational potential energy A pendulum has a mass of 700 g and a length of 50 cm. It is pulled out to an angle of 30° from the vertical. ( |\ ) a) Find the gravitational potential energy stored in the pendulum bob b) The pendulum is released. Find the maximum speed of the pendulum bob as it passes the vertical position. Assume there is no air resistance.
a) ∆h = 0.5 - (cos30 x 0.5) = 0.0669m E grav = 0.7 x 0.0669 x 9.81 E grav = 0.46 = 0.5 J (1s.f.) b) Energy is conserved, so all GPE is converted to KE KE = 0.46 J 0.46 = 1/2 x 0.7 x v^2 v^2 = 0.46/(0.5 x 0.7) v = 1.15 = 1 m/s (1 s.f.)
Example: Work done Q1) A traditional narrowboat is drawn by a horse walking along a canal towpath. The horse pulls the boat at a constant speed between two locks which are 1500 m apart. The tension in the rope is 100 N at 45° to the direction of motion. a) Calculate the work done on the boat. [2 marks] b) It take 31 minutes for the horse to pull the boat between the two locks. Calculate the power supplied to the boat. [2 marks]
a) cos45 x 100N = 70.7N Wd = 70.7 x 1500 W = 106,066 J = 100,000 J (1 s.f.) b) 31 minutes = 1860 s P = W / t P = 106,066 / 1860 P = 57.02 W = 60 W (1 s.f.)
Example: F = ma Q) A boat is moving across a river. The engines provide a *force of 500 N at right angles* to the flow of the river and the boat experiences a *drag of 100 N* in the *opposite direction*. The *force on the boat due to the flow of the river is 300 N*. The mass of the boat is 250 kg. a) Calculate the magnitude of the resultant force acting on the boat. [2 marks] b) Calculate the magnitude of the acceleration of the boat. [1 mark]
a) Force perpendicular to river flow = 500 - 100 = 400 N [1 mark] Force parallel to river flow = 300 N Resultant force = √400^2 + 300^2 = 500 N [1 mark] b) ∑F = ma so a = ∑F ÷ m = 500 ÷ 250 = 2 ms-2 [1 mark]
Example: conservation of energy Q1 A skateboarder is skating on a half-pipe. He lets the board run down one side of the ramp and up the other. The height of the ramp is 2.0 m. a) Calculate his speed at the lowest point of the ramp. Assume friction is negligible. [3 marks] b) State how high he will rise up the other side of the half-pipe. [1 mark] c) Real ramps are not frictionless. Describe what the skater must do to reach the top on the other side. [1 mark]
a) GPE loss = KE gain (energy is conserved) 1/2mv^2 = mgh (cancel out m on both sides) 1/2v^2 = gh v^2 = 2gh v^2 = 2 x 9.81 x 2 = 39.24 v = 6.24 = 6.2 m/s b) 2m (assuming there is no friction) c) Add some energy by pushing the board
Example: A stream provides a constant *acceleration of 6 ms-2*. A toy boat is pushed directly against the current and then released from a point *1.2 m upstream* from a small waterfall. Just *before* it reaches the waterfall, it is *travelling at a speed of 5 ms-1*. a) Calculate the initial velocity of the boat. [2 marks] b) Calculate the maximum distance upstream from the waterfall the boat reaches. [2 marks]
a) Take upstream as negative: v = 5 ms-1, a = 6 ms-2, s = 1.2 m, u = ? use: v2 = u2 + 2as 52 = u2 + 2 × 6 × 1.2 [1 mark] u2 = 25 - 14.4 = 10.6 u = -3.255... = -3 ms-1 (to 1 s.f.) [1 mark] b) From furthest point: u = 0 ms-1, a = 6 ms-2, v = 5 ms-1, s = ? use: v2 = u2 + 2as [1 mark] 52 = 0 + 2 × 6 × s s = 25 ÷ 12 = 2.083... = 2 m (to 1 s.f.) [1 mark]
Example Q: A car accelerates steadily from rest at a rate of 4.2 ms-2 for 6.5 seconds. a) Calculate the final speed. b) Calculate the distance traveled in 6.5 seconds.
a) Using equation v = u + at v = 0 + 4.2 x 6.5 v = 27.3 m/s = 27 m/s (2 s.f.) b) Using equation s = (v+u)t/2 s = 6.5(27.3 + 0)/2 s = 88.725 m = 89 m (2 s.f.)
Example Q: A tile falls from a roof 25.0 m high. Take g = 9.81 ms-2. a) Calculate its *speed when it hits the ground* b) *and how long it takes to fall*.
a) Using v2 = u2 + 2as v = √02 + 2x9.81x25 *velocity = 22.1 m/s (3 s.f.)* b) Use velocity to find time using equation s = (u+v)t/2 2(25) = (0+22.1)t t = 50/22.1 t = 2.26s (3 s.f.)
Example Q: A skydiver jumps from an airplane when it is flying horizontally. She accelerates due to gravity for 5.0 s. a) Calculate her maximum vertical velocity. (Assume no air resistance.) [2 marks] b) Calculate how far she falls in this time. [2 marks]
a) a = - 9.81 ms-2, t = 5.0 s, u = 0 ms-1, v = ? use : v = u + at v = 0 + 5.0 × - 9.81 [1 mark] v = -49.05 = -49 ms-1 (to 2 s.f.) [1 mark] (It's negative because she's falling downwards and we took upwards as the positive direction - You can take down as the positive direction tho.) b) v = -49.05, a = -9.81 ms-2, t = 5.0, u = 0, s=? using: s = (v+u)t/2 s = (-49.05 + 0)x5/2 s = -122.625m = 120m (2 s.f.)
Why do projectiles follow a curved path (2)?
because they have two separate parts to their motion : 1) *constant horizontal velocity* 2) *constant* acceleration vertically *(acceleration due to gravity)*
What is the equation for gravitational field strength
g = F/m g(N/k or ms-2) = Force (N) / mass (kg)
What is the momentum equation?
p=mv Momentum (kg m/s) = mass (kg) x velocity (m/s) (momentum is a vector, so has size and direction)
What is Newton's second law? (force equation)
resultant force (N) = mass (kg) x acceleration (m/s2) ∑F = ma - more force, more acceleration (assuming m constant) - more mass, less acceleration (assuming m f constant)
What is the center of gravity of an object
the *single point* that you can consider its *whole weight to act through* (whatever its orientation).
What is free fall
when the *only force acting on a falling object is gravity* - STUFF ONLY FEELS GRAVITY *Objects undergoing free fall on Earth have an acceleration of g = 9.81 ms-2.* *g* is always *downwards* so it's usually *negative*
CORE PRACTICAL 1: Determine the acceleration of a freely-falling object Evaluation
• *Assuming No air resistance because SMALL AND HEAVY BALL* so very little air resistance • *Small t values*: use *larger distance to reduce uncertainty* • *Time delay between the timer starting* and the *ball being released* due to *RESIDUAL MAGNETISM* in ball: use a *lower current* so that the electromagnet has a *weaker magnetic field * • Having a *computer automatically release and time* the ball-bearing's fall can measure times with a *smaller uncertainty* than if you tried to drop the ball and time the fall using a stopwatch (*reduces human/random error)*
CORE PRACTICAL 1: Determine the acceleration of a freely-falling object Safety
• If *dropping off of a table*, *clamp electromagnet stand to table* to *prevent it toppling* over • Be aware of *falling ball *- use a *tray to capture ball* at the bottom • *Small currents* used in circuit - *no danger of electrical shock*
