Problem 1

The next two questions pertain to the situation described below.

Your car is stuck in a mud. You are alone, but you have a long, strong rope. Having studied

physics, you tie the rope tautly to a telephone pole and pull on it sideways.

(a) Find the force exerted by the rope on the car when the angle θ is 13° and you are pulling with

a force of 105 N but the car does not move.

(b) How strong must the rope be (what is the maximum force the rope should be able with

withstand) if it takes a force of 775 N to move the car when θ = 2°?

Problem 2

The next five questions pertain to the situation described below.

A box of mass m2 = 3.1 kg rests on a frictionless horizontal shelf and is attached by strings to

boxes of masses m1 = 1 kg and m3 = 2.6 kg as shown below. Both pulleys are frictionless and

massless. The system is released from rest. After it is released, find the following.

(a) the acceleration of each of the boxes a1, a2, a3

(b) the tension in each string T1, T2

Problem 2 (continued)

Problem 3

The next three questions pertain to the situation described below.

A 57-kg block is suspended from a uniform chain that is hanging from the ceiling. The mass of

the chain itself is 16 kg, and the length of the chain is 1.5 m.

(a) Determine the tension in the chain at the point where the chain is attached to the block.

(b) Determine the tension in the chain midway up the chain.

(c) Determine the tension in the chain at the point where the chain is attached to the ceiling.

Problem 4

The next two questions pertain to the situation described below.

You fly a model airplane of mass 0.647 kg that is attached to a horizontal string. The plane

travels in a horizontal circle of radius 5.01 m. (Assume the weight of the plane is balanced by the

upward "lift" force of the air on the wings of the plane.) The plane makes 1.2 revolutions every

3.93 s.

(a) Find the speed at which the plane flies.

(b) Find the force exerted on your hand as you hold the string (assume the string is massless).

Problem 5

The next five questions pertain to the situation described below.

In a loop-the-loop ride a car goes around a vertical, circular loop at a constant speed. The car has

a mass m = 286 kg and moves with speed v = 13.82 m/s. The loop-the-loop has a radius of R = 8

m.

a) What is the magnitude of the normal force on the care when it is at the bottom of the circle?

(But as the car is accelerating upward.)

b) What is the magnitude of the normal force on the car when it is at the side of the circle

(moving vertically upward)?

c) What is the magnitude of the normal force on the car when it is at the top of the circle?

d) Compare the magnitude of the cars acceleration at each of the above locations:

a. abottom > aside > atop

b. abottom = aside = atop

c. abottom < aside < atop

e) What is the minimum speed of the car so that it stays in contact with the track at the top of the

loop?

Problem 5 (continued)

Problem 5 (continued)

Problem 6

The next four questions pertain to the situation described below.

Scientists want to place a 4200 kg satellite in orbit around Mars. They plan to have the satellite

orbit a distance equal to 1.6 times the radius of Mars above the surface of the planet. Here is

some information that will help solve this problem:

mmars = 6.4191 x 1023 kg

rmars = 3.397 x 106 m

G = 6.67428 x 10-11 N-m2/kg2

a) What is the force of attraction between Mars and the satellite?

b) What speed should the satellite have to be in a perfectly circular orbit?

c) How much time does it take the satellite to complete one revolution?

d) Which of the following quantities would change the speed the satellite needs to orbit at?

a. the mass of the satellite

b. the mass of the planet

c. the radius of the orbit

Problem 6 (continued)