Wednesday, November 14, 2012

Physics 101 Sample Quiz Solutions

A crate is given an initial push up the ramp of a truck. It starts sliding up the ramp with an initial velocity
vo, as shown in the diagram. The coefficient of kinetic friction between the box and the ramp is !k. The angle is ! = 300. !s = 0.7.

A) Will the magnitude of the acceleration of the sliding crate be greater on the way up or on the way
back down the ramp? Or will the accelerations be the same? Explain using appropriate free-body
diagrams. (5)

B) If the initial speed is 5 m/s, the crate has mass 55-kg, and μk = 0.35, what is the acceleration? (5)

C) How fast will the crate be moving after 0.5 seconds? (5 points)

D)Where will the crate stop? (5pts)

E) Will it slide back down? Why or why not? (5)

A) If there is friction, the free-body diagrams for “sliding up” and “sliding down” are different.

Just looking at the components of force parallel to the ramp:
So the magnitude of the acceleration is bigger when the box is
sliding up the ramp. One way to think of this is that the gravity
and the friction are more lined up when the box is sliding up.
We aren’t supposed to use the word “deceleration” in Phys1101,
but you could say the magnitude of the deceleration when the
box slides up is larger than the magnitude of the acceleration
when the box slides down.

B) The initial speed doesn’t matter here, but direction does. If we use the tilted coordinate system
(see page 124, example 4.5) with positive x pointing up the ramp, then we have n = mg cos(!)
from the y-equation and -mg sin(!) - μk mg cos(!) = ma from the x-equation. The mass cancels,
leaving the acceleration: a = -g sin(!) - μk g cos(!) = -7.9 m/s2.

C) Assume the ramp is long enough. Use v = v0 + at = 5 m/s - 7.9 m/s2 (0.5 sec)2 = 1.1 m/s.

D) Use v2 = v02 + 2a"x giving "x = 1.6 meters when v=0 at the point where the crate stops.

E) When v=0, is static friction enough to hold the box? We know the maximum force of fraction is
fs_max = μsn = μs mg cos(!). The component of the weight pointing down the ramp is mg sin(!).
So who wins, gravity or friction? Since μs mg cos(300) > mg sin(300), friction wins, no backslide.
Phys 1101 sample quiz
Phys 1101 Sample Quiz 3 1

Problem 2. (25 points) A 150-N bird feeder is supported by three cables as shown.

A) Draw a careful free-body diagram. (5 points) (B) Find the tension in each cable. (5 points)

C) Is the horizontal component of the pull of the left cable on the feeder greater than, less than, or
equal to the horizontal component of the pull of the right cable? Explain your reasoning. (5)

D) If the bird feeder were hanging in an elevator, accelerating upward at 1.7 m/s2, would the tension
increase, decrease, or stay the same? Calculate the new tensions in the cables. (10)

C) The horizontal components of the tensions must cancel, so F_total = 0.

D) This is equivalent to setting the gravitational acceleration g = 9.8+1.7 m/s2, i.e. g = 11.5
m/s2. All the tensions need to increase by a factor of 11.5/9.8 = 1.2 roughly.

Phys 1101 sample quiz

Phys 1101 Sample Quiz 3 2

Multiple Choice. Choose the best answer. Five points each.

1. A person pulls a block across a rough horizontal surface at a constant
speed by applying a force F. The arrows in the diagram below correctly
indicate the directions, but not necessarily the magnitudes of the various
forces on the block. Which of the following relations among the force
magnitudes W, k, N, and F must be true?

C. F>k and N<W

2. Blocks A and B, each with a mass of 1.0 kg, are hung from the ceiling of an
elevator by ropes 1 and 2. What is the force exerted by rope 1 on block A when
the elevator is traveling upward at a constant speed of 2.0 m/s? (Use g=10 m/s2)

a) 2 N, b) 10 N, c) 12 N, d) 20 N, e)22 N

3. A small car is pushing a larger truck that has a dead battery. The mass of the truck is
larger than" the mass of the car. Which of the following statements is true?"

A) The car exerts a force on the truck but the truck doesn’t exert a force on the car.

B) The car exerts a larger force on the truck than the truck exerts on the car.

C) The car exerts the same amount of force on the truck as the truck exerts on the car.

D) The truck exerts a larger force on the car than the car exerts on the truck.

E) The truck exerts a force on the car but the car doesn’t exert a force on the truck.

4. All three 50 kg blocks are at rest. Is the tension in rope 2 greater than, less than or
equal to the tension in rope 1?

A) greater than

B) less than

C) equal to

D) none of these
(also, what are the numerical values of T1 and T2?)

4. An elevator that has descended from the 50th floor is coming to a halt at
the 1st floor. As it does, your apparent weight is

A) More than your true weight.

B) Less than your true weight.

C) Equal to your true weight.

D) Zero.

5. A 2.0 kg ball is suspended by two light strings as shown. What is the tension T in the angled
string?

A) 26 N

B) 30 N

C) 9.5 N

D) 20 N.

E) 15 N

Phys 1101

No comments:

Post a Comment