Quarter One Review

1. A child of mass M holds onto a rope and steps off a platform. Assume that the initial speed of the child is zero. The rope has length R and negligible mass. The initial angle of the rope with the vertical is o, as shown in the drawing above.

a. Using the principle of conservation of energy, develop an expression for the speed of the child at the lowest point in the swing in terms of g, R, and cos o

b. The tension in the rope at the lowest point is 1.5 times the weight of the child. Determine the value of cos o.

2. A 0.10-kilogram solid rubber ball is attached to the end of an 0.80 meter length of light thread. The ball is swung in a vertical circle, as shown in the diagram above. Point P, the lowest point of the circle, is 0.20 meter above the floor. The speed of the ball at the top of the circle is 6.0 meters per second, and the total energy of the ball is kept constant.

a. Determine the total energy of the ball, using the floor as the zero point for gravitational potential energy.

b. Determine the speed of the ball at point P, the lowest point of the circle.

c. Determine the tension in the thread at

i. the top of the circle;

ii. the bottom of the circle.

The ball only reaches the top of the circle once before the thread breaks when the ball is at the lowest point of the circle.

d. Determine the horizontal distance that the ball travels before hitting the floor.

3. An automobile engine delivers 24000 watts of power to a car’s driving wheels. If the car maintains a constant speed of 30 m/s, what is the magnitude of the retarding force acting on the car?
(A) 800 N (B) 960 N (C) 1950 N (D) 720,000 N (E) 1,560,000 N

4. A fan blows the air and gives it kinetic energy. An hour after the fan has been turned off, what has happened to the kinetic energy of the air?
(A) it disappears (B) it turns into potential energy (C) it turns into thermal energy
(D) it turns into sound energy (E) it turns into electrical energy

5. A box of old textbooks is on the middle shelf in the bookroom 1.3 m from the floor. If the janitor relocates the box to a shelf that is 2.6 m from the floor, how much work does he do on the box? The box has a mass of 10 kg.
(A) 13 J (B) 26 J (C) 52 J (D) 130 J (E) 260 J

6. A rock is dropped from the top of a tall tower. Half a second later another rock, twice as massive as the first, is dropped. Ignoring air resistance,

(A) the distance between the rocks increases while both are falling.

(B) the acceleration is greater for the more massive rock.

(D) they strike the ground more than half a second apart.

(E) they strike the ground with the same kinetic energy.

7. A 60.0-kg ball of clay is tossed vertically in the air with an initial speed of 4.60 m/s. Ignoring air resistance, what is the change in its potential energy when it reaches its highest point?

(A) 0 J (B) 45 J (C) 280 J (D) 635 J (E) 2700 J

Questions 810

A plane 5 meters in length is inclined at an angle of 37°, as shown. A block of weight 20 newtons is placed at the top of the plane and allowed to slide down.

8. The mass of the block is most nearly
(A) 1.0 kg (B) 1.2 kg (C) 1.6 kg (D) 2.0 kg (E) 2.5 kg

9. The magnitude of the normal force exerted on the block by the plane is most nearly
(A) 10 N (B) 12 N (C) 16 N (D) 20 N (E) 33 N

10. The work done on the block by the gravitational force during the 5meter slide down the plane is most nearly
(A) 20 J (B) 60 J (C) 80 J (D) 100 J (E) 130 J

11.Two blocks of mass 1.0 kg and 3.0 kg are connectedby a string which has a tension of 2.0 N. A force F actsin the direction shown to the right. Assuming friction isnegligible, what is the value of F?

(A) 1.0 N (B) 2.0 N (C) 4.0 N (D) 6.0 N (E) 8.0 N

12.An object in equilibrium has three forces, F1 of 30 N, F2 of 50 N, and F3 of 70 N, acting on it.The magnitude of the resultant of F1 and F2 is

(A) 10 N (B) 20 N (C) 40 N (D) 70 N (E) 80 N

13.A 50-kg student stands on a scale in an elevator. At the instant the elevator has a downwardacceleration of 1.0 m/s2 and an upward velocity of 3.0 m/s, the scale reads approximately

(A) 350 N (B) 450 N (C) 500 N (D) 550 N (E) 650 N

Answers:

1. (a) (b) cos θ = ¾

2. (a) 3.6 J(b) v = 8.2 m/s(c) i) Ft = 3.5 Nii) Ft = 9.5 N(d) 1.6 m

3. A

4. C

5. D

6. A

7. D

8. D

9. C

10. B

11. E

12. D

13. B