Directions:† All questions have equal value.† Do not spend too much time on any one problem.† Do everything that you can do easily, and then return to parts that are harder for you.† If you cannot answer one part of a question that you need for a later part then assume an answer or use a symbol to represent the part that you do not know.†
Useful number(s):††††††††† Gravitational Constant:††††††††††††† G=6.6726x10-11 N◊m2/kg2††††††††
1)†Three masses are place on the corners of a right triangle as shown below.† Assume no other masses are around.† M1=1000kg, M2=2000kg, M3=3000kg.
a) Draw a free body diagram for each mass.
b) Find the total force (vector) on each mass.
2) A car is driving in the rain on a flat road around a curve with a radius of 200m.† When the car slides off the road, a CSI team is called in to investigate.† From the GPS they determine that the car slid of the road when the speed reached 20m/s.† The wreckage is collected and the mass is determined to be 1500kg including the driver.†
a)† Draw a free body diagram for the car just before it slides off the road.† Be sure to indicate which way the car will slide.
b) What was the static coefficient of friction between the car and the road when the car slid off the road?
c) The team suspects that the brakes were not working, but the damage to the car is too extensive to determine directly.† From the skid marks and other information, they know that the car went over a cliff with a speed of 15m/s after traveling 10m from the point the started to slide.† What is the magnitude of the total average force acting on the car during the 10m skid?†††
d) Assuming that the force from part c) is constant and is due to kinetic friction, what is the coefficient of kinetic friction between the car and the road.††
e) (Extra credit) Is kinetic friction enough to account for the carís deceleration from 20m/s to 15m/s? Why or why not?
3) You throw a 1kg ball out of a 4th story window (12m above the ground).† It lands on the ground 5m from the building after 1s.† Ignore air resistance.
a) How fast did you throw the ball?
b) What was the ballís initial velocity vector?
c) How fast was it traveling when it hit the ground?
d) What was the velocity vector when it hit the ground?
e) What was the balls maximum height?
4) A 0.33kg hockey puck (small flat cylinder) is traveling on ice at a velocity of 10m/s due west when it is hit by a hockey stick.† The impact produces a constant force in a direction of 60 degrees south of east and lasts 5ms.† The puck leaves the stick with a velocity direction due south.† Assume that the ice is frictionless. ††††††††
a) What is the magnitude of the force the stick produced?
b) What is the average force vector acting on the stick?
c) What is the speed of the puck when it leaves the stick?
d) What is the average speed of the puck during the contact with the stick?
e) What is the average velocity of the puck during the contact with the stick?
f) What is the average acceleration of the puck during the contact with the stick?
g) What is the total displacement of the puck during contact with the stick?
5) In the diagram above box 1 is 1200kg package that needs to be lifted 10m off the ground. The static friction between box 1 and the ramp is 0.4 and the kinetic friction is 0.2.† Ignore air resistance, and assume massless rope and frictionless massless pulley.†
a) What is the mass of box 2 needed to get box 1 to move?
b) What is the weight of box 2 if it has the mass found in part a)?
c) If box 2 has the mass found in part a) and box 1 is given a small push to start it moving, what is the acceleration vector of Box 1?
d) What is the acceleration vector of Box 2?
6) A 75kg person is in an elevator, standing on a scale measuring their weight in Newtons.† The cable breaks, and the elevator is in free fall.† Ignore air friction.††††††
a) Draw a free body diagram for the person.
b) What weight will the scale read?
c) When the emergency brake takes over the acceleration of the elevator is reduced to 2 m/s/s.† What weight will the scale read?
d) When the speed of the elevator reaches 1 m/s the acceleration is decreased to zero. What weight will the scale read?
e) Finally the elevator is stopped. What weight will the scale read?