PHYSICS 231 CHAPTERS 5-7 TEST 2

Name ________________________
October 9, 2002

1in=2.54cm; v=v₀ + at; g=9.8 m/s²; a*b=ab cosq; a_c=v²/r; V_SPHERE=4/3pr³;
1mi=1.61km; x - x₀=v₀ t + 1/2 a t²; axb=a b sinq; T=2pr/v;
G=6.67x10^-11Nm²/kg²; 1yr=3.16x10⁷s; v²=v₀2 + 2a(x - x₀); dx/dt=v; F_g=Gm₁m₂/r²;
M_Earth=5.97x10²⁴ kg; R_Earth=6380km; x - x₀=1/2(v₀ + v) t; dv/dt=a; T²=(4(2/GM)r³; F_s=m_s N
;
Multiple Choice 3pts each (partial credit if you show your work):
[1] A car rounds a 75-m radius curve at a constant speed of 18 m/s. A ball is suspended by a string from the ceiling of the car and moves with the car. The angle between the string and the vertical is:
A) 0^o B) 1.4^o C) 24^o D) 90^o E) cannot be found without knowing the mass of the ball

[2] A bricklayer is repairing a chimney and his bricks keep sliding off the galvanized steel roof. To keep his bricks from sliding on the slippery roof, which of the following will help:
A) Pile his bricks on top of each other (two layers deep)
B) Stand his bricks up on the narrow end (reduce the surface area of contact)
C) Lay his bricks over on the wide side (increase the surface area of contact)
D) Use smaller bricks (from the same company)
E) None of the above

[3] Block A, with a mass of 10kg, rests on a 35( incline. The coefficient of static friction, (k=0.40. An attached string is parallel to the incline and passes over a massless, frictionless pulley at the top. The smallest mass mB, attached to the dangling end, for which A remains at rest is:

A
B
( = 35(
A) 2.5 kg B) 3.5 kg C) 5.9 kg D) 9.0 kg E) 10.5 kg

[4] Circular freeway entrance and exit ramps are commonly banked to handle a car moving at 30 mph. To design a similar ramp for cars exiting at 60 mph, one should:
A) increase the radius by a factor of 2 D) decrease the radius by a factor of 2
B) increase the radius by a factor of 4 E) decrease the radius by a factor of 4
C) increase the radius by a factor of SQRT(2)

[5] Why do raindrops fall with constant speed during the later stages of their descent?
A) The gravitational force is the same for all drops.
B) Air resistance just balances the force of gravity.
C) The drops all fall from the same height.
D) The force of gravity is negligible for objects as small as raindrops.
E) Gravity cannot increase the speed of a falling object to more than 9.8 m/s.

[6] A crate moves to the right on a horizontal surface as a woman pulls on it with a 10-N force. Rank the situations shown below according to the work done by the 10-N, from smallest to greatest. The displacement is the same for all cases: 10N
10 N
10N
(1) (2) (3)

A) 1,2,3 B) 2,1,3 C) 2,3,1 D) 1,3,2 E) 3,2,1

[7] When a certain rubber band is stretched a distance x, it exerts a restoring force F = ax + bx², where a and b are constants. The work done in stretching this rubber band from x = 0 to x = L is:
A) aL² + bLx³ B) aL + 2bL² C) a + 2bL D) bL E) 1/2 aL² + 1/3 bL³

[8] An astronaut is rotated in a horizontal centrifuge at Cape Canaveral to simulate launch conditions. The centrifuge has a radius of 6.0 m. What is the astronauts speed if the total acceleration that the astronaut feels is 2.0 g?
(A) 2.4 m/s (B) 3.5 m/s (C) 7.7 m/s (D)10 m/s (E) 11 m/s

[9] Satellite 1 is in a certain circular orbit about a planet, while satellite 2 is in a larger circular orbit. Which of the following statements are true? (a) Sat 1 has a larger period than Sat 2; (b) Sat 1 is moving faster than Sat 2.
(A) T,T (B) T,F (C) F,T (D) F,F

[10] You step into an elevator at the Sears tower and notice Einstein is standing on a spring scale at the back. As you head for the observation deck, Einstein tells you that the scale is recording less than his weight. You feel embarrassed for him, because people don't discuss their weight with strangers, but having had physics 231 this semester, you brashly give him 5 reasons for this observation. He said one of your reasons is wrong, which one is it?
(A) The elevator has an upward velocity.
(B) His scale is broken, just like the one in your bathroom.
(C) Gravity is less at the top of the Sears Tower.
(D) The elevator is slowing down as it reaches the top floor
(E) Respiration means one is constantly losing weight due to water vapor and CO₂ loss.

Problems 12pts each: (Do any 6. Extra Credit, do all 7)

[11] Three blocks with kinetic friction coefficient (s=0.5 are connected as shown below on a horizontal table and pulled to the right with a force T3=60.0 N. If m1=12.0 kg, m2=24.0 kg, and m3=36.0 kg, calculate (a) the acceleration of the system and (b) the tensions T1 and T2 in the interconnecting cords.
m1 T1 m2 T2 m3 T3

[12] A 5.0 kg block on an inclined plane is acted on by a horizontal force F with magnitude 50N (see figure below). The coefficient of kinetic friction between block and plane is (k = 0.30. The angle of the inclined plane with the horizontal is ( = 30(. What is the acceleration of the block if it is moving up the plane?

[13] A small bead of mass m is constrained to slide without friction inside a circular vertical hoop of radius r which rotates about a vertical axis at a frequency f. (a) Determine the formula for the angle ( where the bead will be in equilibrium, that is, where it will have no tendency to move up or down along the hoop. (b) If f=3.0 revolutions per second, and r=20cm, what is ( ? (c) Is it possible to get the bead to the midpoint of the hoop (90degrees) or higher? Explain.

[14] Every few hundred years, all the planets line up on one side of the Sun, which was the opportunity that launched the Voyager spacecraft. Doomsday prophets warn of great cataclysms on the Earth, earthquakes and floods for this event. Calculate the net force on the Earth due to the planets Venus, Jupiter and Saturn. Their masses are given as ratios of Earths as follows: Mv = 0.815Me, Mj=318Me, Ms=95.1Me, and the distance from the Sun for V/E/J/S are 108Gm, 150Gm, 778Gm, and 1430Gm. Are the prophets correct? Why?

[15] The Sun rotates about the center of the Milky Way Galaxy at a distance of about 30,000 light years from the center (1 ly = 9.5x1015 m). (a) If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our galaxy is concentrated mostly in a central uniform sphere. (b) If all the stars had about the same mass as our Sun (2x1015 kg), how many stars would there be in our Galaxy.

[16] An airplane pilot fell 370m after jumping without his parachute opening. He landed in a snowbank creating a crater 1.1m deep, but survived with only minor injuries. Assuming the pilots mass was 75kg and his terminal velocity was 47m/s, estimate (a) the work done by the snow in bringing him to rest. (b) the average force exerted on him by the snow, and (c) the work done on him by air resistance as he fell.

[17] A mass m is attached to a spring which is held stretched a distance x by a force F, and then released. The spring compresses, pulling the mass. Assuming there is no friction, determine the formula for the speed of the mass m when the spring returns (a) to its normal unstretched length (x=0); (b) to half its original extension (x/2).