October 21, 1996 Physics 201

EXAM 2

Print your name and section clearly on all five pages. (If you do not know your section number, write your TA's name.) Show all work in the space immediately below each problem. Your final answer must be placed in the box provided. Problems will be graded on reasoning and intermediate steps as well as on the final answer. Be sure to include units wherever necessary, and the direction of vectors. Each problem is worth 25 points. In doing the problems, try to be neat. Check your answers to see that they have the correct dimensions (units) and are the right order of magnitude. You are allowed one 5" x 8" note card and no other references. The exam lasts exactly one hour.

(Do not write below)

SCORE:

Problem 1: __________

Problem 2: __________

Problem 3: __________

Problem 4: __________

TOTAL: ___________

Possibly useful information:

acceleration due to gravity at the earth's surface: g = 9.80 m/s2

PROBLEM 1

A karate expert breaks a 0.14 kg board with his 0.70 kg fist. Treat the board as a spring with spring constant k = 4.1 x 104 N/m, and assume the fist sticks to the board and both stop motion exactly when the board breaks. The board breaks when deflected by 16 mm.

a. How much energy is stored in the board when it breaks? (5 pts.)

b. What is the speed of the fist and board together immediately after impact? (5 pts.)

c. What is the speed of the fist immediately before impact? (5 pts.)

d. Board-fist contact lasts 0.12 s. Find the average magnitude of force on the fist.(5 pts.)

e. If an additional constant frictional force of 243 N acts while the board is bending, with what speed must the fist strike the board? (5 pts.)

PROBLEM 2

A uniform helicopter blade (I = (1/3)ML2) of mass 110 kg and length (axle to tip) 7.80 m is rotating at 320 rev/min. Uniform resistive torque brings it to rest in 6.7 sec (ignore air resistance).

a. Calculate the resistive torque that stops the blade. (5 pts.)

b. How much work did the resistive torque do in stopping the blade? (5 pts.)

c. What was the maximum power used by the torque? (5 pts.)

d. What is the centripetal force per unit mass at the blade tip at 320 rev/min ? (5 pts.)

e. Find themagnitude of force on the bolt holding the blade to the axle at 320 rpm. (5 pts.)

PROBLEM 3

A 500 kg elevator cab descends at constant speed of 4.0 m/s. Its cable suddenly begins to slip, allowing it to fall with constant downward acceleration of g/5. After it falls 12 m, the safety rails are clamped with a normal force of 3.7 x104 N, bringing the cab to rest by friction (mk = 0.25).

a. During its fall, what is the work done on the cab by the force of gravity? (5 pts.)

b. During its fall, what is the work done on the cab by the pull of the cable? (5 pts.)

c. During its fall, what is the total work done on the cab? (5 pts.)

d. What is the speed of the cab at the end of the 12 m fall ? (5 pts.)

e. How far does it travel after clamping the rails? (note: cable is still pulling) (5 pts.)

PROBLEM 4

A 1600 kg car travels around a flat circular road at constant speed 25.0 m/s at a radius of 190 m.

a. What is the minimum ms between tires and road to prevent the car slipping? (5 pts.)

b. What is the magnitude of the total force exerted by the road on the car? (5 pts.)

c. The car now brakes with uniform force and stops after traveling 160 m. What is the braking force? (5 pts.)

d. What is the braking power when the brakes are first applied ? (5 pts.)

e. Assuming the car tires of radius 29 cm do not skid, what is their angular acceleration during braking? (5 pts.)