University Physics UC Davis Spring 2013

7/28/2019 University Physics UC Davis Spring 2013

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Part I: Conceptual Multiple Choice

1. Your car breaks down, and you are forced to push it into the nearest gas station. For a period of time as you are

pushing it, the car is moving at a constant velocity. During this period, which of the following is true?

a. Your push contributes to a non-zero net force on the car that keeps it rolling forward.

b. Newtons 3rd Law ensures that there is an equal-and-opposite force on the car that opposes your push,

making the net force on the car equal to zero.

c. The static friction force by the road on the tires of the car (which are rolling without slipping) is pushing

the car forward.

d. If the car had twice the mass, and you pushed it with the same force, then during that period of time when

the car is moving at a constant velocity Newtons 2nd Law states that it will be moving half as fast as the

case above.

e. None of the above is true.

2. A block hanging from a spring bounces up and down. Assuming no air resistance, which of the following

quantities is conserved for this system throughout the motion of the block?

a. linear momentum

b. kinetic energy

c. mechanical energy (KE + PE)

d. all of these quantities are conserved

e. none of these quantities is conserved

3. A wheel whose axis is vertical (i.e. the plane of the wheel is parallel to the ground) rotates clockwise as viewed

by someone looking down at it. If a small nudge is given to the top of the axis of this wheel toward the south,

which way does the top of the axis move in its immediate response to this nudge? [Hint: Drawing a diagram

may help.]

a. north

b. south

c. east

d. weste. It doesnt move at all the gyroscopic effect keeps it pointing up.

4. A satellite orbits the Earth such that it remains above the same point on the equator at all times. Another

satellite orbits the Earth at a distance (from the Earths center) that is 4 times as far as the previous satellite.

How long does it take the second satellite to orbit the Earth?

a. 4 days

b. 8 days

c. 16 days

d. 64 days

e. Not enough information provided.

Physics 9A Final Exam December 13, 2012


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5. A marble rolls back-and-forth between two ramps located on

opposite ends of a horizontal surface, as in the diagram to the

right. Three graphs of the marbles one-dimensional motion

(its position is measured along the surface) are provided.

Select the graph that best describes this motion as a function

of time. Assume the marble starts (t=0) as shown in the

diagram.

v

t

v

t

v

t

v

t

v

t

6. A small stone slides around inside a horizontal, circular, frictionless track. The track is flexible, and can be

compressed to a smaller radius or expanded to a larger one. If, while the stone is going around, the radius of the

track is shrunk to one-half its previous size, what happens to the kinetic energy and magnitude of the angular

momentum of the stone measured relative to the center of the circle?

a. Both quantities are conserved (i.e. neither one changes).

b. The magnitude of angular momentum increases while the KE stays the same.

c. The KE increases while the magnitude of angular momentum stays the same.

d. Both quantities increase.

e. Impossible to tell without the moment of inertia of the track.


x=0

vo

+x

a.

b.

c.

d.

e.


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7. A rectangular block that is twice as long as it is wide is placed so that one of its

ends is flat against a wedge that makes an angle of 45 degrees with the

horizontal (see diagram to the right). For the block to remain at the same place

on the wedge without falling over, which of the following conditions can make

this possible? [Assume the only forces acting on the block are gravity, the

normal force by the wedge, and a static friction force by the wedge.]

a. The bock will stay where it is with no special conditions thanks to Newtons

1st Law

b. The block may be accelerating (along with the wedge).

c. The blocks mass may not be uniformly distributed.

d. Both (b) and (c) are possible.

e. There is no physical way that the block can fail to tip over without another force being present to act on it.

8. Below are graphs of two potential energy functions U(r) and V(r), which are drawn on identically-scaled axes.

Consider two identical particles, A and B. A is trapped in potential U and is oscillating about the

equilibrium point. B is in a similar predicament in potential V. Both particles have the same total energy.

Which of these comparisons of the motions of the two particles is accurate?

a. A oscillates with a higher frequency than B, and is moving faster at the equilibrium point than B.

b. A oscillates with a higher frequency than B, and is moving slower at the equilibrium point than B.

c. A oscillates with a lower frequency than B, and is moving faster at the equilibrium point than B.

d. A oscillates with a lower frequency than B, and is moving slower at the equilibrium point than B.

e. A and B oscillate with the same frequency and move at the same speed past the equilibrium point.

U(r) V(r)

rr



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Part II: Problem-Solving

9. The frame of a badminton racquet is constructed from two identical thin aluminum rods of uniform density,

massM, and lengthL. One of the rods is bent into a circle and is welded to the end of the other rod.

a. Find the position of the center of mass of this racquet. Give the answer in terms ofL, measured from the

attachment point of the two pieces.

b. Find the moment of inertia of the racquet around an axis located at the point of attachment perpendicular tothe plane of the circle.

10. The potential energy function for a force acting on an object moving in one dimension is given by the equation:

U x( ) = 8.64N( )x (2.00Nm2 )x3

a. Find the positionx of the object where the force on it vanishes.

b. Find the work done on the object by this force as it moves fromx=1.00m to 3.00m.

c. Is the object moving faster atx=1.00m or 3.00m? Briefly explain.

11. A block of mass 0.400kg sits atop an identical block, which rests on a horizontal frictionless surface. The

bottom block is attached to a massless string, which passes over a massless, frictionless pulley and is connected

to a hanging weight (see diagram below). The coefficient of static friction between the two blocks is 0.750.

Find the largest mass that can be hung from the string such that when it is released the top block does not slide

off the bottom block.

12. Two identical systems of blocks on springs are side-by-side as shown in the diagram below. They are set into

motion such that just as they reach their maximum displacements toward each other, they barely come into

contact (there is no collision - their springs stop them just as they touch). When they contact, half of the mass

of one is transferred to the other, and their motion continues.

a. If the smaller block takes 1.4s to return to its maximum stretch from the point in time where it contacted the

other block, how long does it take the larger block to make the round trip?

b. How much energy is transferred between the two systems during the mass hand-off? Show or explain.

13. A solid uniform sphere starts from rest and rolls without slipping down a slope to a horizontal surface an

elevation that is 3.6m below its starting point. It takes 6.6s for it to get down the slope. Find the angle the slope

makes with the horizontal.

14. A constant force is given by the vector: F

= 12.0N( )i 7.5N( ) j. An object at rest is pivoted at the origin

around the z-axis, and the force given above is exerted on the object acts at the pointx=1.2m,y=1.8m.a. Find the torque (magnitude and direction) on the object due to this force.

b. If the object has a moment of inertia about thez-axis equal to 7.8kg-m2, find its angular speed at t=3.00s.


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University Physics UC Davis Spring 2013