Autumn 2000

Student Performance

1. (20 points)

A solid cylindrical pulley of mass M = 5.50 kg and radius R = 0.660 m is used to lower a bucket of mass m = 3.10 kg into a well. See the schematic of the system below.

a.(5 points) What is the linear acceleration a of the bucket?

b.(5 points) What is the tension T in the string?

c.(5 points) What is the angular acceleration of the cylinder?

d.(5 points) Suppose the bucket starts from rest and falls for 4.00 seconds.

How far does it drop?

Solution: See solutions to to #1 of sample test 3.

Answers (a) 5.15 m/s2 (b) 14.28 N (c) 41.56 rad/s2 (d) 41.6 m

2. (20 points)

A liquid flows through two horizontal sections of tubing joined end to end. In the first section the crossectional area is A1 = 9.5 cm2 , the fluid speed is 265 cm/s and the pressure is P1 = 1.2x105 N/m2. In the second section the crossectional area is A2 = 9.0 cm2.

Find the pressure P2 in the second (smaller) section.

Solution: See solutions to #4 of sample test 3
Answer: 1.2x105 N/m2

 

3. ( 20 points) 4.9x104 J of heat is added to an ice cube of mass mICE = 50.0 g at 00C until the ice cube completely melts and becomes part water and part steam at 100oC. The mass of the steam is mST. What is mST ? Cw = 4186 J/kgoC, LF = 3.33x105 J/kg and Lv=2.26x106 J/kg

Solution: See #20, Quiz 10. The only difference is that on the final, you are solving for the mass. Answer: MST = 5 grams

4. (20 points) A block of aluminum of mass m = 5.0 kg is heated from 20oC to 900C at atmospheric pressure. Patm = 1.01x105 N/m2 . Aluminum Density = 2700 kg/m3 .

(a) (10 points) Find the work W done by the aluminum.
Use

(b) (5 points) Find the amount of heat Q transferred to it.
C = 900 J/kg0C

(c) (5 points) Find the increase in the internal energy.

Solution: See#20 of Hints to Q11

Answer: (a) 0.94 J (b) 315 kJ (c) about 315 kJ since Q is much larger than W.

5. (20 points) The motion of an object is described by
x = 0.30 m cos()

(a) (5)What is the position at t = 0 ?

(b) (5)What is the position at t = 0.60 sec ?

(c) (5)What is the frequency f of the motion?

(d) (5)The period T of the motion ?

(e) Extra Credit . (15) What is the time t when x = 0.20 m ?
Hint: Divide both sides by 0.30. Evaluate cos-1 and find t.

Solution: See#23 of Hints to Q12
(a) 0.30 m (b) 0.29 m (c) 0.083 Hz (d) 12 sec (e) 1.6 sec