December 21, 1996 Physics 201
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 magnitude. You are allowed one 8.5” x 11” sheet and no other references. The exam lasts exactly two hours.
(Do not write below)
SCORE:
Problem 1: __________
Problem 2: __________
Problem 3: __________
Problem 4: __________
Problem 5: __________
Problem 6: __________
Problem 7: __________
Problem 8: __________
TOTAL: ___________
Possibly useful information:
Acceleration due to gravity at the earth's surface: g = 9.80 m/s2
Gravitational constant: G = 6.67 x 10-11 N·m2/kg2
Gas Constant: R = 8.31 J(mol-1)K-1
PROBLEM 1
A bullet leaves the muzzle of a gun 2 meters above the level ground traveling horizontally. It strikes the ground 600 meters away. Ignore air resistance in your answers to the following:
a. For how much time was the bullet in flight? (5 pts.)
b. What was the speed of the bullet when it left the gun? (5 pts.)
c. At what angle from the horizontal did the bullet strike the ground? (5 pts.)
d. What is the ratio of kinetic to potential energy (relative to the ground) of the bullet when it was fired? (5 pts.)
e. If the gun barrel was 70 cm long, what was the (assumed constant) acceleration of the bullet while it was in the gun barrel? (5 pts.)
PROBLEM 2
A 2-kg block is connected by a string to a 1-kg block, and they both slide down a plane inclined at an angle of 30. The lower (2-kg) block has no friction, and the upper (1-kg) block has = 0.6.
a. What is the magnitude of the acceleration of the blocks? (15 pts.)
b. What is the tension in the string? (10 pts.)
PROBLEM 3
A block of mass 680 g is attached to a spring with spring constant 65 N/m. It is pulled a distance 11 cm away from its equilibrium position.
a. What is the period of oscillation? (5 pts.)
b. What is the maximum speed of the block? (5 pts.)
c. What is the maximum acceleration of the block? (5 pts.)
d. What is the potential energy of the block when it is 5.5 cm from equilibrium? (5 pts.)
e. What is the kinetic energy of the block when it is 5.5 cm from equilibrium? (5 pts.)
PROBLEM 4
A 100-kg car traveling 20 m/s collides head-on with a 2000-kg truck initially at rest, and the car rebounds with a speed of 4 m/s in the opposite direction.
a. What is the speed of the truck just after the collision? (5 pts.)
b. What is the magnitude of the impulse on the car? (5 pts.)
c. If the collision lasts 0.4 seconds, what is the average deceleration of the car? (5 pts.)
d. What fraction of the kinetic energy is lost in the collision? (5 pts.)
e. Where does the kinetic energy lost in the collision go? (5 pts.)
PROBLEM 5
A 3-kg circular ring is released from rest from the top of a 1-m-high ramp inclined at an angle of 20 and rolls down the ramp without slipping.
a. What is the total kinetic energy of the ring when it reaches the bottom of the ramp? (5 pts.)
b. What fraction of this energy is in translation of the center of mass? (5 pts.)
c. What is the speed of the center of mass when the ring reaches the bottom of the ramp? (5 pts.)
d. What is the magnitude of the acceleration of the center of mass while the ring is rolling down the ramp? (5 pts.)
e. How much time does it take for the ring to reach the bottom of the ramp? (5 pts.)
PROBLEM 6
One proposal for a manned mission to Mars is to assemble a space station in earth orbit from which a mission would be launched.
a. Given that the radius of the earth is Re = 6370 km, use the information on the cover page to calculate the mass of the earth. (5 pts.)
b. Calculate the work required to place a 1-kg mass into a circular low-earth (h << Re) orbit. (10 pts.)
c. Calculate the additional work required for the 1-kg mass above to escape completely from the earth's gravity. (10 pts.)
PROBLEM 7
Four moles of N2 (an ideal diatomic gas with molecular mass 28 g/mole) undergo a temperature increase from 300 K to 360 K under constant pressure.
a. How much heat was added to the gas? (5 pts.)
b. By how much did the internal energy of the gas increase? (5 pts.)
c. How much work was done by the gas? (5 pts.)
d. By how much did the translational kinetic energy of the gas increase? (5 pts.)
e. What is the rms velocity of the N2 molecules at 360 K? (5 pts.)
PROBLEM 8
A 2-kg block of ice at 0 C is heated until it melts and then further heated until the water is turned into steam at 100 C.
a. What volume of liquid water is produced when the ice melts? (5 pts.)
b. What volume of steam is produced, assuming the pressure is 1 atmosphere (1.013 x 105 N/m2)? (5 pts.)
c. What total heat is required? (5 pts.)
d. What is the change in entropy when the ice melts? (5 pts.)
e. What is the change in entropy when the liquid water is heated from 0 C to 100 C? (5 pts.)