These are a small group of questions that I hope will help you check on your skills and solidify your understanding of the principles. Correct answers are underlined.

1. A 5-kg ball of radius 10 cm slides along the floor. If the ball's speed is 2 m/s, what is its total kinetic energy? Notice that the problem is a little different from the version I handed out in class. The reason is that if the ball rotates, there is additional KE.

Use KE = (1/2)mv² to get (1/2)(5 kg)(2 m/s)² = 10 J

2. A 40 gram point mass swings with a period T = 4.0 s at the end of a cord of length L. If this mass is changed to 120 gm, the new period is ___ s.

(1) 1.0 (2) 2.0 (3) (4) 4.0 (5)

As you saw in the lab, the period does not depend on the mass

3. A person on a scale weighs 600 N in a stationary elevator.

a) What does the scale read if the elevator moves upward at a constant velocity of 3 m/s?

There is no change since the acceleration is zero

b) What does the scale read if the elevator moves downward but slows at the rate of 2 m/s each second?

Ans: The acceleration is 2 m/s² in the upward direction. This means that the person feels as if he is in a world where the effective value of g is 12 m/s² instead of 10 m/s². His weight is therefore (12/10) times 600 N, or 720 N. If this answer escapes you, think of Newton’s 2^nd law. The free-body diagram of the person should have two forces, 600 N downward and an unknown force F upward exerted by the scale. These two forces produce an upward acceleration of 2 m/s². Newton’s 2^nd law is then F – 600 = m(2 m/s²). Since m is 60 kg, we again find F = 720 N.

4. A cart moves from x = 4 m to x = 8 m, then reverses direction, stopping at x = 2 m. The elapsed time for this motion is 5 s. The average speed for this 5 s is ___ m/s.

(1) 1.6 (2) -2 (3) 2 (4) -0.4 (5) 0.4

Speed is the total distance traveled divided by the total time. The total trip is 10 m in 5 s

5. In the above question, the average velocity for the cart for the 5 s interval is ___ m/s.

(1) 1.6 (2) -2 (3) 2 (4) -0.4 (5) 0.4

Velocity is the net distance traveled divided by the time. Thus v = (-2 m)/(5 s) = -0.4 m/s.

6. A rock that is tossed upward at a velocity of 25 m/s will hit the ground in ___ s.

(1) 2 (2) 2.5 (3) 3 (4) 4 (5) 5

Since the rock slows down at the rate of 10 m/s each second, the rock’s upward velocity is zero at t = 2.5 s. The total trip is thus 5 s.

7. A car has a velocity of 30 ft/s, when suddenly it is given an acceleration of -10 ft/s² until the car comes to rest. From that moment, the car travels an additional ___ ft.

(1) 45 (2) 60 (3) 75 (4) 90 (5) none of these

The car will come to rest in 3 seconds. During this time period, the average velocity is 15 m/s. Since this average velocity occurs over a time span of 3 s, the distance covered is 45 m.

8. A person pushes horizontally with +200 N of force on a 40-kg box sliding on a level rough surface. The box pushes back on the person with a force of magnitude ____ N.

(1) less than 200 (2) 200 (3) more than 200 (4) not enough data to tell

Now matter what, the 3^rd law reaction force is also 200 N, but in an opposite direction.

9. A ball moving 15 m/s rolls off the end of a table 1 1/4 m high. How far from the base of the table is the ball expected to hit the floor? Hint: Remember when I used the blowgun?

The ball will be in flight for exactly the same amount of time as a ball dropped from a height of 1.25 m. Use d = (1/2)gt² to get a fall time of ½ s. The ball maintains its horizontal velocity of 15 m/s as it falls. The ball therefore goes (15 m/s)(½ s) = 7.5 m.

8. In a calculation, you find units of acceleration in the denominator and units of velocity in the numerator. Your answer must have units of ____.

(1) length (2) velocity (3) time (4) 1/length (5) 1/time

(m/s)/(m/s²) = s

9. The dimensions (or units) of two quantities must be identical if you either ______ the quantities.

(1) subtract or divide (2) multiply or divide (3) add or multiply
(4) add or subtract (5) all of these

10. A stone is tossed straight upward at an initial speed of 30 m/s. Assuming the acceleration of gravity to be 10 m/s², the stone's speed after 4 seconds is ____m/s.

(1) 5 (2) 10 (3) 15 (4) 20 (5) 25

Since the stone slows at 10 m/s each second, after 3 s the velocity is zero, after which it reverses direction ans speeds up at 10 m/s each second.

11. A 4-kg object is given a kinetic energy of 16 Joules. The object could have acquired this 16 Joules of kinetic energy by falling through a vertical distance of ____ m. Assume g = 10 m/s².

(1) 1/4 (2) 2/5 (3) 1/2 (4) 2/3 (5) 1

This KE could have been as a result of losing potential energy of PE = mgh, where h is the vertical distance through which the object fell. Thus, 16 J = mgh, giving h = (16 J)/(40 N) = 2/5 m.

12. The dimensions (or units) of two quantities must be identical if you either ____ the quantities.

(1) subtract or divide (2) multiply or divide (3) add or multiply
(4) add or subtract (5) all of these -----oops! Just like question 9

13. A graph of velocity for a certain object as a function of time is shown below. The acceleration for this object is ___ m/s² .

(1) 4/3 (2) 3/4 (3) -4/3 (4) -3/4 (5) none of these

Answer: The slope of the line is the acceleration, which is –3/4 m/s².

14. A cart moving +10 m/s in a straight line is given an acceleration of +4 m/s² for a time interval of exactly 2 seconds. During this time interval the cart moves ____ meters.

(1) 28 (2) 32 (3) 36 (4) 40 (5) none of these

This is similar to question 7. The average velocity during the 2-second interval is 14 m/s.

15. Consider the following data for the five objects, A,B,C,D and E, which are moving horizontally at a height of 10 meters above the level ground:
m_A = 1 kg, v_A = 10 m/s; m_B = 2 kg, v_B = 8 m/s; m_C = 3 kg, v_C = 6 m/s;
m_D = 4 kg, v_D = 5 m/s; m_E = 5 kg, v_E = 3 m/s.

Which one of these objects has the most potential energy? E, the one with most mass

Which one of the above objects has the most kinetic energy? B, the one with most mv².

Which one of the above objects has the most momentum? D, the one with most mv.

16. Two twins, A and B, pull on opposite ends of a rope. Twin A exerts a force F and succeeds in dragging twin B along the ground. Which one or more of the following are true?
a) The force twin B exerts on his end of the rope is smaller than F.
b) Twin A is able to push harder on the ground than is twin B.
c) The tension in the rope is 2F.

(1) a (2) b (3) c (4) a and b (5) b and c

This requires understanding of Newton’s 2^nd law and 3^rd law. The rope tension is F, by definition.

17. A force F = 3 N acts for 2 seconds on a 4-kg mass sliding along a level floor. During this time interval the mass slides 5 meters. The total work done during the time interval is ___ J.

(1) 6 (2) 8 (3) 12 (4) 15 (5) 20

Work done is the product of the force acting over a distance of 5 m. W = Fd = (3 N)(5 m) = 15 J.

18. An elevator is pulled upward at an acceleration of 2 m/s² by means of a cable. If the cable tension is 1800 N, the elevator must have a mass of ___ kg.

(1) 50 (2) 75 (3) 100 (4) 125 (5) 150

Apply Newton’s 2^nd law, as in question 3. The net force is (1800 N – mg). Thus, the expression for the 2^nd law is 1800 N – mg = ma. We wish to find m, knowing that a = 2 m/s² upward. You should get m = 150 kg.

19. If you do 100 J of work in 50 s, what is your power output?

Power is defined as the rate of doing work. In this case, power = (100 J)/(50 s) = 2 J/s = 2 watts

20. A hydraulic press, like a simple lever, properly arranged, is capable of multiplying energy input. This statement is

(1) sometimes true (2) always false (3) always true

The statement violates the law of conservation of energy!!!!

21. How much farther will a car going twice as fast as another skid with locked brakes?

A car going twice as fast has 4 times as much KE. In both cases the stopping force of the skidding tires is the same value. Therefore, the skidding force must act over 4 times the distance.