PHYS 407 Final

Angular Acceleration

a/r

Torque (T)

IA rxF rFSinO

Angular Momentum (L)

IW rxp for a single mass

Rotational Kinetic Energy

(1/2)IW^2

Spring Potential Energy

(1/2)k(xf-xi)

Linear Kinetic Energy

(1/2)mv^2

As I sled down a frictionless hill, which of the following statements is true (select all that apply): (a) total mechanical energy is conserved. (b) potential energy is conserved. (c) Kinetic energy is conserved. (d) kinetic energy minus potential energy is conserved

(a) because no energy is lost as friction or heat PE not conserved because the height changes KE not conserved because the velocity changes KE and PE are changing inversely, meaning the difference gets smaller, then they are equal, then it gets larger again

You are standing on a skateboard, initially at rest. A friend throws a very heavy ball towards you. You can either catch the object or deflect the object back towards your friend (such that it moves away from you with the same speed as it was originally thrown). What should you do in order to MINIMIZE your speed on the skateboard? A) Catch the ball. B) Deflect the ball. C) Your final speed on the skateboard will be the same regardless whether you catch the ball or deflect the ball.

A) Catch the ball

On a smooth horizontal floor, an object slides into a spring which is attached to another mass that is initially stationary. When the spring is most compressed, both objects are moving at the same speed. Ignoring friction, what is conserved during this interaction? A) momentum and mechanical energy B) momentum only C) kinetic energy only D) momentum and kinetic energy E) momentum and potential energy

A) Momentum and Mechanical Energy

A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii and are of uniform density. If the three are released simultaneously at the top of an inclined plane and roll without slipping, which one will reach the bottom first? A) solid sphere B) hollow pipe C) solid cylinder D) They all reach the bottom at the same time.

A) Solid Sphere

When you ride a bicycle, in what direction is the angular velocity of the wheels? A) to your left B) to your right C) forwards D) backwards E) up

A) To your left

When a rigid body rotates about a fixed axis, all the points in the body have the same A) tangential speed. B) angular acceleration. C) tangential acceleration. D) linear displacement. E) centripetal acceleration.

B) Angular Acceleration

Two identical balls are thrown directly upward, ball A at speed v and ball B at speed 2v, and they feel no air resistance. Which statement about these balls is correct? A) Ball B will go twice as high as ball A because it had twice the initial speed. B) Ball B will go four times as high as ball A because it had four times the initial kinetic energy. C) The balls will reach the same height because they have the same mass and the same acceleration. D) At its highest point, ball B will have twice as much gravitational potential energy as ball A because it started out moving twice as fast. E) At their highest point, the acceleration of each ball is instantaneously equal to zero because they stop for an instant.

B) Ball B will go four times as high as Ball A because it had four times the initial kinetic energy. Why? KE=(1/2)mv^2 so if v=2v, then with the squared int he equation it becomes 4v^2

If two forces of equal magnitude act on an object that is hinged at a pivot, the force acting farther from the pivot must produce the greater torque about the pivot. A) true B) false C) unable to decide without knowing the shape of the object

B) False

Consider a plot of the displacement (x) as a function of the applied force (F) for an ideal elastic spring. The slope of the curve would be A) the spring constant. B) the reciprocal of the spring constant. C) the acceleration due to gravity. D) the reciprocal of the acceleration of gravity. E) the mass of the object attached to the spring.

B) The reciprocal of the Spring Constant (see Hooke's Law)

A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass, compressing the spring a distance x. After it is released, the box slides up a curved frictionless incline and eventually stops. If we repeat this experiment but instead compress the spring a distance of 2x A) the box will go up the incline twice as high as before. B) just as it moves free of the spring, the box will be traveling twice as fast as before. C) just as it moves free of the spring, the box will be traveling four times as fast as before. D) just as it moves free of the spring, the box will have twice as much kinetic energy as before. E) just before it is released, the box has twice as much elastic potential energy as before.

B) just as it moves free of the spring, the box will be traveling twice as fast as before

If the torque on an object adds up to zero, (a) the object could be accelerating linearly but it could not be turning. (b)the object is at rest. (c) the object could be both turning and accelerating linearly. (d) the object cannot be turning. (e) the forces on it also add up to zero.

C

A 4.0-kg object is moving with speed 2.0 m/s. A 1.0-kg object is moving with speed 4.0 m/s. Both objects encounter the same constant braking force, and are brought to rest. Which object travels the greater distance before stopping? A) the 4.0-kg object B) the 1.0-kg object C) Both objects travel the same distance. D) It is impossible to know without knowing how long each force acts.

C) Both objects travel the same distance

A dumbbell-shaped object is composed by two equal masses, m, connected by a rod of negligible mass and length r. If I1 is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and I2 is the moment of inertia with respect to an axis passing through one of the masses, it follows that A) I1 = I2. B) I1 > I2. C) I2 > I1.

C) I2 > I1

A small glider is coasting horizontally when suddenly a very heavy piece of cargo falls out of the bottom of the plane. You can neglect air resistance. Just after the cargo has fallen out A) the plane speeds up and the cargo slows down. B) the plane speeds up but the cargo does not change speed. C) neither the cargo nor the plane change speed. D) the cargo slows down but the plane does not change speed. E) both the cargo and the plane speed up.

C) Neither the cargo nor the pane change speed

Consider two less-than-desirable options. In the first you are driving 30 mph and crash headon into an identical car also going 30 mph. In the second option you are driving 30 mph and crash head-on into a stationary brick wall. In neither case does your car bounce off the thing it hits, and the collision time is the same in both cases. Which of these two situations would result in the greatest impact force? A) hitting the other car B) hitting the brick wall C) The force would be the same in both cases. D) We cannot answer this question without more information. E) None of these is true.

C) The force would be the same in both cases

Swimmers at a water park have a choice of two frictionless water slides as shown in the figure. Although both slides drop over the same height, h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v1 of a swimmer reaching the end of slide 1 compares with v2, the speed of a swimmer reaching the end of slide 2? A) v1 > v2 B) v1 < v2 C) v1 = v2 D) No simple relationship exists between v1 and v2 because we do not know the curvature of slide 2.

C) V1=V2

Is it possible for a system to have negative potential energy? A) Yes, as long as the kinetic energy is positive. B) Yes, as long as the total energy is positive. C) Yes, since the choice of the zero of potential energy is arbitrary. D) No, because the kinetic energy of a system must equal its potential energy. E) No, because this would have no physical meaning.

C) Yes, since the choice of zero is arbitrary i.e. if you choose a point above the object as your zero height, the object will possess negative potential energy.

A stock person at the local grocery store has a job consisting of the following five segments: (1) picking up boxes of tomatoes from the stockroom floor (2) accelerating to a comfortable speed (3) carrying the boxes to the tomato display at constant speed (4) decelerating to a stop (5) lowering the boxes slowly to the floor. During which of the five segments of the job does the stock person do positive work on the boxes? A) (1) and (5) B) (1) only C) (1), (2), (4), and (5) D) (1) and (2) E) (2) and (3)

D) (1) and (2) Why? Because the object is accelerating in the same direction as the person

Two stones, one of mass m and the other of mass 2m, are thrown directly upward with the same velocity at the same time from ground level and feel no air resistance. Which statement about these stones is true? A) The heavier stone will go twice as high as the lighter one because it initially had twice as much kinetic energy. B) Both stones will reach the same height because they initially had the same amount of kinetic energy. C) At their highest point, both stones will have the same gravitational potential energy because they reach the same height. D) At its highest point, the heavier stone will have twice as much gravitational potential energy as the lighter one because it is twice as heavy. E) The lighter stone will reach its maximum height sooner than the heavier one.

D) At its highest point, the heavier stone will have twice as much gravitational potential energy as the lighter one because it is twice as heavy

Three cars (car F, car G, and car H) are moving with the same velocity when the driver suddenly slams on the brakes, locking the wheels. The most massive car is car F, the least massive is car H, and all three cars have identical tires. Which car travels the longest distance to skid to a stop? A) Car F B) Car G C) Car H D) They all travel the same distance in stopping.

D) They all travel the same distance in stopping. Why? Friction is proportional to the normal force which, in this case, is proportional to the weight

Two men, Joel and Jerry, push against a wall. Jerry stops after 10 min, while Joel is able to push for 5.0 min longer. Compare the work they do. A) Both men do positive work, but Joel does 75% more work than Jerry. B) Both men do positive work, but Joel does 50% more work than Jerry. C) Both men do positive work, but Jerry does 50% more work than Joel. D) Both men do positive work, but Joel does 25% more work than Jerry. E) Neither of them does any work.

E) Neither of them does any work

As a tile falls from the roof of a building to the ground its momentum is conserved. True or False?

False

If two non-zero vectors point in the same direction, their dot product must be zero. True or False?

False

If two vectors are perpendicular to each other, their cross product must be zero. True or False?

False

The value of the dot product of two vectors depends on the particular coordinate system being used. True or False?

False

In a collision of two objects, mechanical energy is always conserved. True or False?

False because energy can be lost as heat, sound, deformation, etc

I move a crate on the floor five meters from x=0 m to x=5 m. there is a frictional force of magnitude 200 N acting against my push. Therefore, the potential energy due o friction when the crate is at x=5 m is 1000 J. True or False?

False because there is not Potential energy due to friction

If a force always acts perpendicular to an object's direction of motion, that force cannot change the object's kinetic energy. True or False?

True

If the dot product of two non-zero vectors is zero, the vectors must be perpendicular to each other. True or False?

True

When an object is solely under the influence of conservative forces, the sum of its kinetic and potential energies does not change. True or False?

True

Gravitational Potential Energy

mgh

Linear Momentum (p)

mv

Tangential Acceleration

rA

Arc length

rO

Tangential Velocity

rW

Angular Velocity

v/r