Sample Test 3 from Sp ‘11

1. (40 points) Testing a car for the Loop-the-Loop ride.
A un-manned test car whose mass m is 250.0 kg rolls without friction around a track at Great America amusement park. It starts from rest at the point shown on the inclined ramp. The ramp merges into the vertical circle of radius R = 20.0m m shown. The car rolls down the ramp, rounds the track counter-clockwise and goes through points A, B, D and C in that order of time. At point A, the magnitude N of the normal force on the car is 7 times the weight of the car.

(a) (15 points) What is the magnitude N of the normal force at point B, which is at the end of a horizontal diameter?

(b) (15 points) What is the magnitude N of the normal force at point C at the highest point on the circle?

(c) (3 points) At point B what is the magnitude a_RAD and direction of the radial acceleration ?

(d) (3 points) At point B what is the magnitude | a_t | and direction of the tangential acceleration ?

(e) (4 points) What is the speed of the car at point D where the dashed radial line shown makes an angle of 45 degrees with the vertical?

2. (40 points) At the instant shown, a 2.00-kg block with speed
v = 3.00 m/s is about to contact an uncompressed, massless parallel spring. The spring has force constant k = 125.00 N/m and is attached to a wall. The diagram below shows time sequence shots of the block moving toward the spring plate just before contact and at the point of maximum compression of the spring. The coefficient of kinetic friction between ground and bottom of the block is µ = 0.100.

(a) (26 points) Find the maximum distance D (in m) the spring will be compressed.

(b) (10 points) What is the work done be friction (in (Joules) during this motion? Is this work positive or negative? Explain.

(c) (4 points) How far from the point of maximum compression shown will the block travel to the right before finally coming to rest?

3. (40 points) Pushing a Cat Part II.

Your Cat “Ms.” (mass m = 7.00 kg, represented by box below ) is trying to make it to the top of a frictionless ramp. The ramp is 2.00 m long and inclined upward at 30.0 degrees with the horizontal. At point A (the bottom) the cat starts with running speed 2.40 m/s directed upward along the incline. Since the poor cat cannot get any traction on the ramp, you push her along the ramp but apply a steady horizontal force of magnitude F = 125.00 (N). See below diagram showing the cat moving upward along the incline; the distance between points A and B is 2.00 m. For full credit on this problem you must use energy related methods in Chapter 6 or 7. Otherwise you will lose points.



(a) (4 points) What is the work W_g done on the cat by gravity during her motion from A to B?
(b) (36 points) What is the cat’s speed when she reaches the top (point B) ?

(c) (5 points) Extra Credit. Compute the speed at the top (B) in the presence of friction. Assume the cat starts at the bottom (A) with the same speed 2.40 m/s. Repeat part (b) if the coefficient of kinetic friction between the cat and inclined surface is µ = 0.150. Explain the difference between the cat’s speed at the top in this case and the speed you computed in part (b).