First Name: ___________________ Last Name: ____________________ Section: _________

May 14, 1998 Physics 103

 

Final Exam

Print your name and section clearly on all nine 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 magnitudes. You are allowed two 8½ x 11" sheets of notes and no other references. The exam lasts exactly 2 hours.

(Do not write below)

 

SCORE:

 

Problem 1: __________

 

Problem 2: __________

 

Problem 3: __________

 

Problem 4: __________

 

Problem 5: __________

 

Problem 6: __________

 

Problem 7: __________

 

Problem 8: __________

 

 

TOTAL: ___________

First Name: ___________________ Last Name: ____________________ Section: _________

1. A block is released from rest and slides without friction down a plane inclined at an angle q from the horizontal. It reaches the bottom of the incline 3 seconds after it was released moving with a speed of 14.7 m/s.
 

 

 

 
 

a. Calculate the distance traveled by the block. (15 pts.)
 

 

 

 

 

 

 

 

 

 

 

 

 

 
 
 
b. Calculate the angle q. (10 pts.)

 

 

 

 

 

 

 

 

 

 

 

 
 

 

 First Name: ___________________ Last Name: ____________________ Section: _________

2. Two masses are connected by a massless string that passes over a massless, frictionless pulley as shown. The 4-kg mass accelerates downward at 5 m/s2.

 

a. Calculate the coefficient of kinetic friction between the 2-kg mass and the table. (15 pts.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
b. Calculate the tension in the string. (10 pts.)  

 

 

 

 

 

 

 

 

 

 

 

 

 

First Name: ___________________ Last Name: ____________________ Section: _________

3. Raindrops are falling at a speed of 100 m/s from a cloud 4 km above the ground and accumulating on the ground at a rate of 1 cm/hr over a circular region of diameter 10 km.

a. What total mass of water falls in one hour? (8 pts.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b. How many watts of heat are produced by friction of the rain with the air? (9 pts.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

c. If the heat calculated above is all absorbed by the water, what is its temperature rise? (8 pts.)

 

 

 

 

 

 

 

 First Name: ___________________ Last Name: ____________________ Section: _________

4. A 2000-kg automobile traveling north at 15 m/s collides with a 1500-kg automobile traveling east at 20 m/s. The automobiles stick together after the collision.

a. What is their velocity after the collision? (15 pts.)
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

b. How much kinetic energy is lost in the collision? (10 pts.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

 First Name: ___________________ Last Name: ____________________ Section: _________

5. A 2000-kg automobile with four-wheel drive and weight distributed equally on the four 60-cm diameter wheels can accelerate from 0 to 27 m/s (60 MPH) in 6 seconds.

a. Calculate the minimum coefficient of static friction between the tires and the ground. (10 pts.)

 

 

 

 

 

 

 

 

 

 

 

 
 

 

b. What torque is required on the wheels to achieve this acceleration? (10 pts.)

 

 

 

 

 

 

 

 

 

 

 
 

 

c. Repeat the calculation in part (a) assuming the automobile has two-wheel drive. (5 pts.)

 

 

 

 

 

 

 

 

 

 First Name: ___________________ Last Name: ____________________ Section: _________

6. A circular pond 10 meters in diameter and 2 m deep contains water at 30°C at sea level.

a. If the molecular weight of water is 18 g/mole, how many molecules of water are in the pond? (5 pts.)

 

 

 

 

 

 
 
b. Calculate the pressure at the bottom of the pond. (5 pts.)  

 

 

 

 
 

 

c. What is the mass of a cubic block of wood 10 cm on a side that floats on the pond with 75% of its volume submerged? (5 pts.)

 

 

 

 

 
 

 

d. How much energy is required to evaporate all the water in the pond? (5 pts.)

 

 

 

 

 
 

 

e. What is the change in entropy of the water during evaporation? (5 pts.)

 

 

 

 
  First Name: ___________________ Last Name: ____________________ Section: _________
7. A thin horizontal wire supports a uniform massive beam hinged at the bottom as shown. The beam is 3 m long and has a mass of 80 kg.

 
 

a. Calculate the tension in the wire. (15 pts.)
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

b. What is the lowest frequency of vibration of the wire if the wire is 5 m long and has a mass of 0.5 kg? (10 pts.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 First Name: ___________________ Last Name: ____________________ Section: _________

8. You discover that your TA has a pet goose, and you decide to take out your frustration with physics by having the goose for dinner.

a. Assuming the goose has a mass of 4 kg and a specific heat the same as water, how long must you cook the goose in your 800-W microwave oven to raise its temperature from 20°C to 200°C? (8 pts.)

 

 

 

 

 

 

 

 

 

 
 

 

b. The goose realizes what’s about to happen and flies away at a speed of 20 m/s, making a honking sound at a frequency of 500 Hz. What frequency do you hear? (8 pts.)

 

 

 

 

 

 

 

 

 
 

 

c. If the goose produces 10 mW of sound, estimate how long you can hear the honking. (9 pts.)