Exam 1

1) A worker drags a crate across a factory floor by pulling on 
a rope tied to a crate.The worker exerts a force of 450 N on the 
rope, which is inclined at an angle 38 degrees above the horizontal.
The floor exerts a horizontal force of 125 N that opposes the motion.
If the mass of the crate is 310 kg, what is its acceleration?

2) A 1000 kg boat is traveling at 90 km/h when its engine is shut off. The
magnitude of the frictional force between the water and the boat is 
proportional to the speed of the boat, f = 70v, where v is in m/s
and f is in Newtons. Find the time required for the boat to slow down to
45 km/h.

3) A 100 kg crate is pushed up a ramp inclined at 30 degrees to the 
horizontal by a force in the horizontal direction. If the ramp is 
frictionless, and the box travels up the ramp at constant speed
a) what is the magnitude of the force. b) what force is exerted by
the ramp on the box?

4) You throw a ball at wall of height 25 m at a distance 22 m from
you. If you release the ball at an angle of 40 degrees above the horizontal
from a height 2 m above the ground, what minimum speed must you throw
the ball with in order for it to clear the wall?

5) A helicopter lifts a 72 kg astronaut 15 m vertically from the ocean
by means of a cable. The acceleration of the astronaut is g/10. How much 
work is done on the astronaut by a) her weight and b) the helicopter? 

Exam 2

1) A pendulum consists of a 2 kg stone swinging on a 4 m long string
of negligible mass. The stone has a speed of 8 m/s when it passes its
lowest point. a) What is the speed of the rock when it is at an angle of
60 degrees to the vertical? b) What is the greatest angle with the vertical
that the string will make during the stone's motion?

2) Find the center of mass of a right circular cone of height h, radius R,
and uniform density, assuming that the axis of the cone lies along the 
+y-axis with the tip of the cone at the origin.

3) A cockroach of mass m lies on the rim of a uniform disk of mass
4m that can rotate freely around its center. Initially the disk and 
cockroach rotate together at an angular velocity w. Then, the cockroach walks
halfway to the center of the disk. a) What is the new angular velocity of the 
cockroach-disk system? b) What is the ratio of the new kinetic energy of the
system to its initial kinetic energy? c) What accounts for the change
in kinetic energy?

4) A 3 m long, 240 N, uniform rod is held in a horizontal position by two 
ropes at its ends. The left rope makes an angle of 150 degrees with the rod
and the right rope makes an angle theta with the horizontal. A 90 N
howler monkey hangs motionless 0.5 m from the right end of the rod.
Calculate the tensions in the ropes, and the angle theta.

5) A meter stick is held vertically with one end on the floor and is 
then allowed to fall. Find the speed of the other end just before it
hits the floor, assuming the end on the floor does not slip.

Exam 3

1) The motor of a scout rocket uses up all its fuel and stops when the 
rocket is a height 200 km above the surface of the earth and is moving 
vertically at a speed of 8.5 km/s. How high will the rocket rise above 
the surface of the earth?

2) A small body of mass 0.1 kg is undergoing simple harmonic motion
of amplitude 10 cm and period 0.2 s. What is the maximum value of the
force acting on it?

3) Water is moving at a speed of of 5 m/a through a pipe with a cross-sectional
area of 4 cm-squared. the water gradually descends 10 m as the pipe increases
to 8 cm-squared. What is the flow speed at the lower level?

4) Two trains are traveling toward each other, each moving at a speed 
with respect to the ground of 30 m/s. One train is blowing its horn at
a frequency of 500 Hz. What frequency does the engineer of the other train
hear?

5) A hollow spherical shell of iron floats so that is just completely 
submerged in water. If the outer diameter of the sphere is 60 cm,
what is its inner diameter?