Units and Vectors

A car starts from rest and accelerates at 10 m/s2 for 4 seconds. How far does it travel?

80m

If I am going 20 m/s and I accelerate at 4 m/s2 for 10 seconds, how far will I travel?

400m

A car is continuously driving in a circle of radius 30 meters in a parking lot. How is the centripetal force for this circular motion being generated? A Friction between the tires and the road B Through the centrifugal force C Not enough information D Through the steering wheel

A. When a car turns, friction between the tires and the road is responsible for the change in the car's velocity vector. Despite being less intuitive, this is an identical scenario to all other circular motion scenarios we have discussed: Centripetal force is pointing inwards, directly at the center of the circle, while the car's velocity vector is perpendicular to the centripetal force. The result is circular motion of the vehicle.

Which of the following scenarios does NOT involve a conservative force? A A pen rolls off the table and falls to the floor. B A skydiver reaches a constant, terminal velocity due to air resistance. C A medical student jumps on a trampoline for fun. D A shipping container full of medical supplies is connected to cables and lifted using a crane to transport it from the ship to a truck.

B The skydiver hits a maximum, constant velocity due to the force of air resistance opposing the skydiver's motion. For non-conservative forces, we should be aware of friction, air resistance, and viscosity. In each of these cases, a moving object will slowly lose energy as it works against any of these non-conservative forces. When the skydiver jumps out of the plane, they begin to accelerate due to the force of Earth's gravity (which is conservative). As the skydiver falls at increasingly faster rates, they begin to experience more and more air resistance, which opposed the skydiver's motion. Energy continues to be lost as a result of air resistance on the skydiver, and the skydiver eventually reaches a constant, maximum velocity at which they can fall. This answer is correct because the force that causes the skydiver to reach terminal velocity, the situation specified in the question, is a non-conservative force. Gravitational force is not what causes the skydiver to reach terminal velocity. A pen falls to the floor due to the gravitational force the Earth exerts on it. Gravitational force is an example of a conservative force because it does not matter if the pen falls straight down for bounces off other objects, such as the chair, in a zig-zag pattern when it falls. It will have the same gravitational potential energy regardless of the path it takes to reach the floor because the initial height above the ground and final height above the ground does not change. A trampoline works by harnessing the elastic force stored in a spring when the weight of the medical student stretches the spring and is then sent flying upwards when the stretched springs contract back to their normal resting position. Elastic force is an example of a conservative force because it does not matter if the springs are stretched in small increments broken up by periods of partial relaxation or stretched all the way at one time. The spring will have the same amount of elastic potential energy at its final stretched position regardless of exactly how the spring arrived at that position. The shipping container is lifted via the force of tension in the cables from the crane. Tension is an example of an electrostatic force, which is conservative. The container is also acted upon by gravity as it is lifted from one height to another, and gravity is also a conservative force.

Which of the following is acceleration inversely proportional to? Select all that apply. A Force B Mass C Velocity D Distance per unit time

B. Think, f=ma, thus a=f/m

If a cannonball is fired at 100 m/s at a 30 degree angle above the horizontal, what is the initial vertical velocity? (Note that cos 30 = 0.87 and sin 30 = 0.5.)

Because velocity in the y-direction is equal to sinθ times the total velocity, we can do the following calculations:vy = vi sinθvy = (100 m/s) sin(30)vy = 50 m/s

A motorcyclist initially traveling at 70 m/s accelerates at a constant acceleration to a speed of 130 m/s in 10 seconds. How far did he travel? A 400 m B 600 m C 800 m D 1000 m

D

What is the gravitational force acting between a 4 x 105 kg medical research space station and a 6 x 1022 kg asteroid if they are 5 x 104 m apart? A (G)(1.0 x 1011 kg2/m2) newtons B (G)(9.6 x 1018 kg2/m2) newtons C (G)(5.0 x 1023 kg2/m2) newtons D (G)(5.0 x 1019 kg2/m2) newtons

For cases not involving an object on the surface of the Earth, we need to use the following equation. Forcegravitational = (G)(m1)(m2)/r2 where G is the universal gravitational constant, m1 is the mass of one object, m2 is the mass of the other object, and r is the distance between the two objects. Remember to convert values given to SI units (kilograms and meters) prior to using this equation. Plugging in the provided values to the following equation yields: Forcegravitational = (G)(6 x 1022 kg)(4 x 105 kg) / (5 x 104 m)2 = (G)(24 x 1027 kg2) / (25 x 108 m2) = ~(G)(1 x 1019 kg2/m2) Be careful with your estimation here! We rounded the numerator up to 25 x 1027 kg2 in order to get approximately (G)(1 x 1019) newtons. When you round the numerator up, it means that your estimated answer is going to be slightly larger than the true answer. This means that on the MCAT, you want to select an answer choice that is slightly less than (G)(1 x 1019) newtons if one is available. In this case, the true value will be (G)(0.96 x 1019) = (G)(9.6 x 1018) newtons.

How long will it take for a ball to hit the ground if it is thrown vertically up in the air at a velocity of 50 m/s?

For the first half of the ball's flight, the initial velocity will be 50 m/s and the final velocity will be equal to 0 m/s (as it reaches the peak of its flight). Acceleration will be g, and will be causing the ball to slow down, so we can use the value of -10 m/s2. vf = vi + at(0)= (50) + (-10) t-50 = -10tt = 5 seconds. However, that is only the first half of the flight! The ball must come back down, which will take the same amount of time as it took to go up. Thus, the total flight time will be 10 seconds.

If power is an amount of force applied over a distance in a certain amount of time, by which of the following terms would you multiply units of force to get units of power?

Force is measured in Newtons (N) and equal to the mass (kg) of an object multiplied by the acceleration (m/s2) of that object. Therefore, 1 N = (kg)(m/s2). Power is measured in (newton)(meter)/(second). Following standard SI notation, the units for power would be: [(kg)(m/s2)(m)]/(s) = kg(m2/s3). The question wants us to identify what units we need to multiply by a newton to get the unit for power. If we were to multiply (m/s) by a newton, we would get kg(m2/s3), which is the unit for power.

Free body diagram section

Free body diagram section

What is the gravitational force a 35 kg person exerts on the Earth? (Note the gravitational constant G = 6.67 x 10-11 m3/kg*s2).

Gravity is an attractive force that exists between any two masses. Every piece of matter in the universe exerts some amount of gravitational attraction on every other mass. This means the Earth exerts an attractive force on us, and we also exert an equal and opposite attractive force on Earth. When discussing the gravitational attraction between the Earth and an object on its surface, we can calculate gravitational force as Force=(mass)(acceleration due to gravity) = (35 kg)(10 m/s2) = 350 N. The Earth exerts a 350 N force on this person and this person exerts a 350 N force on the Earth.

What force will need to be applied to start sliding a 60 kg patient from rest in one bed to the next if the coefficient of static friction is 0.75? A 45 N B 80 N C 450 N D More than 450 N

In order to determine how much force needs to be applied, we need to calculate the force that must be overcome. Since we are concerned about starting to move the patient from rest, we need to overcome the force of static friction. We can use the following equation: Fstatic = μN. Fstatic is the force due to static friction, μ is the coefficient of static friction, and N is the normal force. Fstatic = μN = (0.75)(60 kg)(10 m/s2) = (3/4)(600 N) = (1800 N/4) = 450 N If the patient is going to be moved, this 450 N force of static friction must be overcome, so physicians and nurses moving the patient must apply a force greater than 450 N.

What kind of horizontal force acts between the powered tires of a car accelerating slowly on dry pavement without an incline, and the road? A Gravity B Kinetic friction C Static friction D Normal force

Static friction Note, Intuitive answers in physics are surprisingly rarely correct. One may think of a car as being in motion, and therefore expect to encounter kinetic friction - but the tires themselves are in constant, static contact with the ground under normal operation. Abnormal circumstances, either due to slippery roadways, other surfaces or intentional driver action, are called skidding, sliding or drifting, among others.

Which of the following will cause the force of friction to increase? Select all that apply. A Increasing the coefficient of friction B Decreasing the coefficient of friction C Increasing the weight of the object D Putting the object on a 45° incline instead of a flat surface

The force due to friction is given by the equation F = µN, where µ is the coefficient of friction and N is the normal force. Increasing the coefficient of friction would therefore increase the force due to friction. A useful way to conceptualize this concept is to think of the coefficient of friction as an intrinsic property of a material that can be distilled down to how "sticky" something is. The force due to friction is given by the equation F = µN, where µ is the coefficient of friction and N is the normal force. The normal force is the force perpendicular to the surface upon which the object rests. The normal force is equal and opposite to the weight of the object, so N = mg. Therefore, increasing the weight of the object will increase the normal force acting on it and consequently increase the force due to friction. Incorrect Answer The force due to friction is given by the equation F = µN, where µ is the coefficient of friction and N is the normal force. The normal force is the force perpendicular to the surface upon which the object rests. The normal force is equal and opposite to the weight of the object, so on an incline N = mg cos (θ). If the angle is increased to 45°, the normal force will decrease because cos(45°) is roughly 0.7. Decreasing the normal force will cause a decrease in the force due to friction.

A 15 kg box is sliding down a ramp with an incline of 25 degrees. What is the magnitude of the force from gravity on the box parallel to the incline?

The force from gravity on a box pointing parallel to an incline is equal to (m)(g)sin(theta). Plugging in the numbers in the question, 15*10*sin(25°) = 62 N.

Which of the following will cause the normal force between a cat and the surface it is sitting on to decrease? A Increasing the mass of the cat B Increasing the angle of incline for the surface the cat is sitting on to 15° C Increasing the coefficient of static friction D Raising the cat from the floor to a position on a table that is 5 m higher off the ground

The normal force is the force exerted between two surfaces in contact, at an angle perpendicular to those surfaces, that prevents them from passing through each other. If the surface the cat is sitting on is horizontal, the normal force must be equal to the force of gravity on the cat, since gravity pulls the cat perpendicularly into the surface. However, if the surface is at an angle, the force of gravity does not point perpendicularly into the surface; you could imagine splitting it into two components, one pointing perpendicularly into the surface and the other pointing parallel to the surface, and only the component pointing into the surface will be opposed by the normal force. At such an angle of incline, the component of gravity pointing into the surface (which will have the same magnitude as the normal force) will be equal to (mass)(acceleration due to gravity)(cosθ). Because cosθ is equal to 1 at no incline and is less than 1 at any nonzero angle of incline up to 90°, the normal force will decrease when the angle of incline is increased. Note that at 90°, the normal force goes to zero; this is the case where the surface is completely vertical, so it doesn't support the cat at all! Incorrect Answer A This would cause the normal force to increase, since the normal force must be larger to support the cat's larger weight.

What pieces of information do you NOT need to know in order to solve for the gravitational force felt by the Earth from a butterfly pollinating flowers? Select all that apply. A Distance between the center of mass of the butterfly and the Earth B Mass of the butterfly C Mass of the Earth D Universal gravitational constant

The only one you need is mass of butterfly, anything else is not needed. Think, you can use f=ma for this one not the complicated other equation. Gravitational force can be expressed by two equations. The more general equation is F= [(G)(m1)(m2)]/r2. However, when finding the force of Earth's gravity on objects near its surface, we can use the shortcut Fg = mg, where all we need to know is the mass of the object and the acceleration due to gravity. We do NOT need to know the universal gravitational constant in this case.

True or False: Deploying a parachute decreases the force of gravity pulling on a skydiver towards the center of the earth.

This statement is false. Deploying the parachute will increase the force of air resistance, but that will not change the force of gravity. The force of gravity will always be equal to mg.

True or false: Two objects exerting an equal and opposite force on each other will experience the same magnitude of acceleration because force and acceleration are directly proportional.

This statement is false. Two objects exerting equal and opposite forces on each other will experience different accelerations if their masses are different. This concept is represented by Newton's second law: Force=(mass)(acceleration). The accelerations will only be the same if the masses are equal. Because this question does not specify what the mass of each object is, we cannot assume that the acceleration will be equal.

A fish is placed on a massless spring with a spring constant of 140 N/m. The spring was initially at rest and is now compressed by 3 centimeters. What is the mass of the fish?

Using Hooke's law, we know Fspring = -kx for the forces acting upwards on the fish, while Fgrav = mg for the downward forces. When the fish is in its final position, we know that Fgrav = Fspring, therefore -kx = mg. Solving for m, this yields m = -kx/g = -140 N/m * 0.03 m / 10 m/s2 ≅ (-1.4 * 3/10) kg ≅ 0.42 kg. The fish weighs approximately 420 grams.

Which of the following values is an accurate conversion of 5 W?

Watts are a unit of power. Power is equal to work, measured in joules, divided by time, measured in seconds. Therefore, W = J/s. Work is equal to force, measured in newtons, times distance, measured in meters. Therefore, W = J/s = N·m/s. Force is equal to mass, measured in kilograms, times acceleration, measured in meters per second squared. Putting this all together, W = J/s = N·m/s = kg·m2/s3. Therefore, 5 W can be expressed in SI base units of 5 kg·m2/s3. 5 kilograms is equivalent to 5000 grams, thus 5000 g·m2/s3 is also equivalent to 5 watts.

What is the coefficient of kinetic friction between the shoe covers used in the operating room and the tile floor, if an 80 kg surgeon goes sliding across the floor at a constant velocity when acted upon by a force of 2300 N?

We can calculate the coefficient of kinetic friction using the equation Fkinetic = μN. The surgeon is sliding at constant velocity, which means they are not accelerating, so there is no net force. No net force means that the forward force causing the surgeon to slide must be perfectly balanced by the force of kinetic friction, which opposes the surgeon's motion. Because of this, we can set Fkinetic = 2300 N. Fkinetic = μN 2300 N = μ (80 kg)(10 m/s2) 2300 N = μ (800 N) 2300 N / 800 N = μ ~3 = μ

what are the non conservative forces

air resistance and friction

If a baseball player throws a ball at 10 m/s at 60 degrees above the horizontal, what is the horizontal distance that the ball will travel before it lands? (sin 60 = 0.87 and cos 60 = 0.5) A 0.5 m B 8.7 m C 50 m D 87 m

b Correct Answer In order to answer this question, we need to find: (1) the initial velocity of the ball in the y-direction, (2) the total time the ball spends in the air, and (3) the velocity of the ball in the x-direction.First, let's calculate the ball's initial vertical velocity:viy = (vi)sinθviy = (10 m/s) sin (60)viy = (10 m/s) (0.87)viy = 8.7 m/s

Gravitational force is conservative or non-conservative?

conservative

electromagnetic force and magnetic force are conservative or non-conservative?

conservative

If a bullet is fired at 10 m/s at an angle of 60 degrees above the horizontal, what will be its horizontal velocity right before it hits the ground? (Note that sin 60 = 0.87 and cos 60 = 0.5.)

vix = vi cosθvix = (10 m/s) cos (60) vix = (10 m/s) (0.5)vix = 5 m/s

Will the acceleration of a mobile x-ray machine be constant if a constant, nonzero net force is applied to push it between inpatient rooms in the hospital? Why?

yes, Newton's second law states that acceleration is directly proportional to the net force applied. If a constant net force is applied to the machine, its acceleration will be constant as well.