Physics 103 exam 2 spinrg 2020

How to solve a problem involving a system in physics:

1) Determine as much as you can about the individual components. 2) Specify the relationships between components. 3) Use those relationships to solve for what you need

How can two children of different weights balance a seesaw?

A: the lighter child must sit farther away from the pivot point while the heavier child sits closer to the pivot point

Consider a stationary series of 5 links of chain being pulled from opposite directions by two forces, Tleft,1 and Tright,5, of equal magnitude, T. What is the net force on the middle link (#3)? Assume that the links have so little mass, we can ignore gravity. A) T B) T/5 C) T/10 D) 0

D) 0 because acceleration equals zero

Which force comprises an action-reaction pair with T4,3? A) Tright,5 B) Tleft,1 C) T2,3 D) T3,4 E) T1,3

D) T3,4

A rocket of mass m rocket forces gas with mass m gas out the back. What is the ratio of the accelerations of the rocket and gas (a rocket/a gas)? A) arocket/agas = 1 B) arocket/agas = 0 C) arocket/agas = mrocket/mgas D) arocket/agas = mgas/mrocket E) I need more information

D) arocket/agas = mgas/mrocket

you have three cases Case 1: 6 kg box conected to a 4 kg box connected to a 2 kg box being pulled Case 2: two 6kg boxes being pushed Case 3: a 12 kg box being pulled In which case is the strength of the push or pull greatest? A. case 1 B. case 2 C. case 3 D. all the same

D. all the same

Which speed is smaller, the one you found in A or the one you found in B? Why? Can you explain?

Since 1 + (m/2M) will always be larger than 1, the velocity of the mass with the pulley that has mass will be smaller. Essentially, the potential energy turned into kinetic energy by the falling mass will now have to be split between the mass itself and the rotational KE of the pulley.

1) Madison is roughly at the 45th parallel in the northern hemisphere. As you sit in your seat, are you moving with more, less, or the same angular velocity as someone sitting down to do physics at the equator? Only consider the rotation of the Earth on its axis here. a) Your angular velocity is larger than that of the person at the equator. b) Your angular velocity is less than that of the person at the equator. c) Your angular velocity is the same as that of a person at the equator. d) You can't tell without knowing height above sea level

You both travel 2π radians in one day c. Your angular velocity is the same as that of a person at the equator.

Below is a free body diagram of the bucket carrying the water. Which of the forces shown are Third-Law pairs? (Nwater is the normal force the water exerts on the bottom of the bucket.) a) T rope,bucket and W earth,bucket b) T rope,bucket and N water,bucket c) W earth,bucket and N water,bucket d) T rope,bucket and the sum of W earth,bucket + N water,bucket e) There are no Third-Law pairs in this diagram.

e) There are no Third-Law pairs in this diagram. There are never Third-Law pairs on the same free body diagram since they must be affecting different objects.

A rotating body or system can be in equilibrium if

its rate of rotation is constant and remains unchanged by the forces acting on it.

approximation—the distances r1 and r2 are the distances to

points directly below the center of gravity of each child.

centripetal acceleration,

refers to changes in the direction of the velocity but not its magnitude. An

Linear or tangential acceleration

refers to changes in the magnitude of velocity but not its direction.

The three types of equilibrium

stable, unstable, neutral

perpendicular lever arm r⊥

the shortest distance from the pivot point to the line along which F acts;

Now let us consider what happens if the fisherman applies a brake to the spinning reel, achieving an angular acceleration of -300rad/s How long does it take the reel to come to a stop?

w=w0 +at t=(w-w0)/a you are told w0=200 w=0

unstable equilibrium

when displaced, it experiences a net force or torque in the same direction as the displacement from equilibrium. A system in unstable equilibrium accelerates away from its equilibrium position if displaced even slightly. An obvious example is a ball resting on top of a hill. Once displaced, it accelerates away from the crest.

relationship between angular acceleration and linear/tangental acceleration

α= a linear/ radius

On a digital video disc (DVD), video and audio data are stored in a series of tiny pits that are evenly spaced along a long spiral that traverses most of the surface of the disc. The scanning laser in a DVD player must read this information at a constant rate. As the player reads information recorded closer and closer to the outer edge of the DVD, the disc A. rotates slower B. rotates at the same speed C. rotates faster.

A. rotates slower

In general, objects with a larger moment of inertia:

Have more mass concentrated away from the axis • Are more difficult to start rotating • Store more kinetic energy in K rot

two crates are at rest and touching each other slightly, a worker pushes on crate 1. Which of the following is a force exerted on Crate 2? a. a force exerted by the worker b. a force exerted by crate 1 on crate 2

b. a force exerted by crate 1 on crate 2

stable equilibrium

when displaced from equilibrium, it experiences a net force or torque in a direction opposite to the direction of the displacement. For example, a marble at the bottom of a bowl will experience a restoring force when displaced from its equilibrium position. This force moves it back toward the equilibrium position. Most systems are in stable equilibrium, especially for small displacements.

What are the magnitudes of the forces pulling in opposite directions on the middle link (#3)? Continue to ignore gravity. A) T B) T/5 C) T/10 D) 0 E) There's not enough information to decide

A) T When we add up forces on a single object, we only have to consider external forces because any force one part of the object exerts on another will be canceled out by an equal and opposite internal force.

Think about the two forces (again, assuming the link is essentially massless) on link #3. Are T2,3 and T4,3 an action reaction pair governed by Newton's 3rd Law? A) Yes B) No C) Yes, but only if link #3 is not moving.

B) No Action-reaction pairs will never appear in the same free body diagram since they are on different objects.

If we send a solid cylinder and a solid sphere with identical masses and radii rolling without slipping down an inclined plane starting from the exact same vertical height up the plane, which one will reach the bottom first? A) The solid cylinder B) The solid sphere C) Both will reach the bottom at the same time.

B) The solid sphere sphere wins because it has smaller I

a car traveling 70 meters/ second down a highway collides with a bug, which of the following is true? A. The car exterts a larger force on the bug than the bug on the car B. The car exerts a same sized force on the bug that the bug exerts on the car C. The car exerts a smaller force on the bug than the bug on the car

B. The car exerts a same sized force on the bug that the bug exerts on the car According to newtons third law, the forces exerted are the same, but the accelerations are different and the fatal acceleration is what kills the bug

The red dot is at the edge of the rotating disk as shown. The green dot is midway between the center and edge. Which has the larger angular velocity ? A) Red dot B) Green dot C) Same for both

C) Same for both

In an Atwood's Machine with two unequal masses, which of these is always true once the masses are moving? A. The tension in the string is equal to both the weight of the heavier mass and the weight of the lighter mass. B. The masses are in motion so there is no tension in the string. C. The answer depends on Newton's Fourth Law and so can't be precisely calculated. D. The tension in the string between the masses is larger than the weight of the lighter mass and less than the weight of the heavier mass. E. The tension in the string between the masses is smaller than the weight of the lighter mass and more than the weight of the heavier mass.

D. The tension in the string between the masses is larger than the weight of the lighter mass and less than the weight of the heavier mass. If the masses are unequal, then one of them must be larger than the other. In this case, once you let go of them, the larger mass will accelerate downward and the smaller mass will accelerate upward. In other words, the larger mass is experiencing a net force down and the smaller mass is experiencing a net force up. If we think about the individual forces on each mass, this means that the weight of the larger mass down must be more than the tension in the string pulling the larger mass up. Likewise, for the smaller mass, the weight pulling the mass down must be less than the tension pulling it up.

True/False: it is sufficent that the net external force of a system be zero for a system to be in equilibrium.

False!: think of a hockey stick lying flat on the ice. if you push it from the same spot on both sides, the net force will be zero and it will be at static equilibrium. however if you push at differant points on differant parts of the hockey stick, it will experience rotational acceleration so it matters where you apply the force

3) You have a choice of two different wheels for your bike. The first have a moment of inertia of 0.01 kg m2 . The second have a moment of inertia of 0.02 kg m2 . If you coast down from the top of a large hill, which will give you the largest speed at the bottom? Assume everything else about the wheels (like internal friction) is the same. a) The first wheels b) The second wheels c) You'll be going the same speed no matter which wheels you use. d) We can't say without knowing the mass of the wheels. e) We can't say without knowing the radius of the wheels.

In this case, you want a rolling object that won't have much rotational kinetic energy. That means you can convert more of your gravitational potential energy into linear kinetic energy. a) The first wheels

What happens if you double the radius of the pulley? Will that affect your answer in B?

It would have no effect. The only thing that matters is the mass of the pulley

Based on your experience in previous questions, if you wanted to ensure that the object was moving with the least speed after falling a distance of Δy (for instance, as a safety measure in designing the pulley at the top of an elevator shaft) would you choose a pulley shaped like a solid disk or one shaped like a hoop? Assume they have the same mass. Also be sure to justify your answer.

It would require more work to get the hoop to rotate, and more of the final kinetic energy of the system would end up in the hoop's rotational KE, so that would minimize the linear kinetic energy of the system. For that reason, you wouldn't want to choose the hoop.

An ice skater is spinning with her arms extended at 1 rev/s. She pulls in her arms and spins at 5 rev/s. What is the ratio of her initial moment of inertia to her final moment of inertia, Iinitial:Ifinal? a)5:1 b) 1:5 c) 1:1

Since angular momentum is conserved, if ω increases, then I must decrease a) 5:1

Which shape should you choose if you want a flywheel that stores the most rotational kinetic energy?

The hoop. Shapes will store different amounts of rotational KE, even if they have the same mass and radius. In general, those with more mass on the rim store more rotational KE.

The radius also matters. For example, the smaller a wheel,

The radius also matters. For example, the smaller a wheel, the smaller its linear acceleration for a given angular acceleration

static equilibrium

a motionless state in which there is no net force or net torque acting This motionless person is in static equilibrium. The forces acting on him add up to zero. Both forces are vertical in this case.

3) What is a Third-Law paired force to any one of the forces in the diagram above? a) The normal force of the bottom of the bucket up on the water. b) The gravitational force of the water in the bucket on the bucket. c) The gravitational force of the water in the bucket on the earth. d) The tension in the rope pulling up on the bucket. e) The tension in the rope pulling on your hands.

a) The normal force of the bottom of the bucket up on the water. Any Third-Law pair with a force on the diagram would have to be a force exerted on something other than the bucket. So we can eliminate b and d. Next, to be a pair with any force by X on the bucket, the paired force would need to be by the bucket on X. So the bucket needs to be exerting the force. That means we can eliminate c (it's the water exerting the force on the earth) and e (it's the rope exerting a force on your hands). That leaves a. The normal force of the bottom of the bucket up on the water is a Third-Law pair with the normal force of the water down on the bottom of the bucket.

In both cases shown, a hula‑hoop with mass MM and radius RR is spun with the same angular velocity ωω about a vertical axis through its center. In Case 1, the plane of the hoop is perpendicular to the rotation axis, and in Case 2, it is parallel. In which case does the spinning hoop have the most kinetic energy?a. Case 1 b. same in both cases c. Case 2

a. Case 1

A hoop, a solid disk, and a solid sphere, all with the same mass and the same radius, are set rolling without slipping up an incline, all with the same initial kinetic energy. The same three objects are set rolling without slipping up an incline, all with the same initial linear speed. Which goes furthest up the incline? a. the hoop b. the solid disk c. the solid sphere d. they all roll to the same height

a. the hoop

Given the same initial and final positions, which wheels would allow a soap‑box derby car to go faster? Assume the mass of the wheels is fixed. a. uniform disks b. ones that are like conventional bicycle tires, with most of the mass along the rim of the wheels

a. uniform disks

weird w

angular velocity

The second condition necessary to achieve equilibrium involves

avoiding accelerated rotation (maintaining a constant angular velocity).

2) A solid sphere and hollow sphere of the same mass and radius are rolling along the floor without slipping at the same linear velocity. Which has the greater rotational kinetic energy? (You can find formulae for the moments of inertia of solid and hollow spheres on the next page.) a) The solid sphere b) The hollow sphere c) They both have the same kinetic energy. d) We can't say without knowing their angular velocities.

b) The hollow sphere Isolid = (2/5)MR2 vs. Ihollow = (2/3)MR2 Ihollow > Isolid so the hollow sphere will have more KE for a given linear velocity, since Krot = ½Iω2

dynamic equilibrium

constant velocity This car is in dynamic equilibrium because it is moving at constant velocity. There are horizontal and vertical forces, but the net external force in any direction is zero. The applied force Fappsize 12{F rSub { size 8{"app"} } } {} between the tires and the road is balanced by air friction, and the weight of the car is supported by the normal forces, here shown to be equal for all four tires.

1) You're lifting a bucket full of water up from the bottom of a well at a constant speed of 0.25 m/s. You stop to take a rest. How much does the tension in the rope decrease when you're resting compared to when you were moving the bucket upward? a) The tension is half. b) The tension is 0.25 times. c) The tension is double. d) The tension is the same. e) The tension is zero.

d) The tension is the same. In both cases, there is no acceleration. That means Fnet = 0 or Tension - Weight = 0, which means Tension = Weight whether you are pulling upward at a constant speed or resting.

A thin, uniform rod of length LL and mass MM rotates around an axis that passes through a point one‑third of the way from the left end, as shown in the figure. What will decrease the rotational kinetic energy of the rod by the greatest amount? a. decreasing the mass of the rod by one‑fourth, while maintaining its length b. decreasing the length of the rod by one‑half, while maintaining its mass c. decreasing the angular speed of the rod by one‑half d. each of the above scenarios will decrease the rotational kinetic energy by the same amount

d. each of the above scenarios will decrease the rotational kinetic energy by the same amount

A hoop, a solid disk, and a solid sphere, all with the same mass and the same radius, are set rolling without slipping up an incline, all with the same initial kinetic energy. Which goes furthest up the incline? a. the hoop b. the disk c. the sphere d. they all roll to the same height

d. they all roll to the same height

neutral equilibrium

equilibrium is independent of displacements from its original position. A marble on a flat horizontal surface is an example. Combinations of these situations are possible. For example, a marble on a saddle is stable for displacements toward the front or back of the saddle and unstable for displacements to the side.

Moment of Inertia

measures how much work it takes to rotate an object (which depends on its mass and its shape). Big I ➔ Takes a lot of work to turn, but stores a lot of rotational kinetic energy for a given " Small I ➔ Doesn't take much work to turn, but doesn't store much rotational kinetic energy for a given "

SI unit of torque is For example, if you push perpendicular(90 degrees) to the door with a force of 40 N at a distance of 0.800 m from the hinges, you exert a torque of.....?

newtons times meters, usually written as N⋅m. 32 N·m(0.800 m × 40 N × sin 90º) relative to the hinges. If you reduce the force to 20 N, the torque is reduced to 16 N⋅m, and so on.

counterclockwise rotation=

positive