Test 1 – PHY1033C – January 27, 2004

 

Answer multiple choice questions in the boxes provided.  For other questions, give a brief calculation, statement or diagram as requested.  There will be partial credit only if you show your work.

 

1. As an object falls freely in a vacuum, the

 

(1) velocity of the object increases  (2) acceleration of the object increases 
(3) the net force on the body decreases  (4) all of these are true  (5) none of these are true

 

When an object falls in a vacuum, the acceleration is constant and has the value g = 10 m/s2 caused by the constant gravitational force.  Because of this, an object’s velocity increases 10 m/s each second.

 

2. A package falls off a truck that is moving at 30 m/s. Neglecting air resistance, the horizontal speed of the package just before it hits the ground is

 

(1) zero   (2) less than 30 m/s but more than zero   (3) about 30 m/s   (4) more than 30 m/s   (5) more information is needed for an estimate

 

As the package falls off, it initially has the velocity of the truck.  The horizontal component of this velocity stays constant (no air resistance).  Only the vertical component changes

 

3. A man pulls with a force F on a rope to drag a box along a level surface.  Assume that the rope is horizontal, that the box slides at constant velocity, and that a friction force Ff acts in a direction opposite the motion.  Which one of the following is correct for the magnitude of F?

(1) F = 0     (2) F is slightly larger than Ff       (3) F is exactly equal to Ff
(4) F is slightly less than Ff   (5) there is not enough information to answer the question

 

As long as the velocity stays constant, the net force must be zero.  The forces F and Ff must be exactly equal and opposite.

 

4. A stone is tossed downward from a high bridge.  The rock is given an initial downward velocity of 10 m/s, and the stone is observed to hit the ground below 2 seconds later.

    a) What is the velocity of the stone just before impact with the ground?

Since the stone’s velocity increases by 10 m/s each second, and since it starts at a velocity of 10 m/s, the velocity 2 seconds later must be 30 m/s.

 

    b) How high is the bridge?

 

The average velocity of the stone is (10 + 30)/2 or 20 m/s.  It has this average velocity for 2 seconds.  Thus, the stone must have fallen 40 meters.

 

5. On a scale in a stationary elevator, Joe weighs 600 N.  Isolate Joe in a sketch.  Then draw and label all the forces acting on Joe for each of the situations below, giving the actual value of each force.

 

Show all the forces acting on Joe if the                                     Show all the forces acting on Joe if the           

elevator moves upward at a constant velocity.                        elevator accelerates upward at 2 m/s2.

 

In case 1, the two forces must be equal and opposite because there is no acceleration.  In case two, there is an upward acceleration of 2 m/s2.  This means that there must be a net upward force of 120 N, implying the force of the elevator floor is larger than before by 120  N.  The value 120 N comes from a ratio.  Knowing that 600 N accelerates Joe at 10 m/s2, one fifth of 600 N will accelerate Joe 2 m/s2.

 

 

 

6. A ball is tossed upwards at a speed of 30 m/s.  At the instant the ball reaches its maximum altitude, which one or more of the following are true?

                a) The gravitational force on the ball is zero   b) The acceleration of the ball is zero 

                c) The velocity of the ball is zero

 

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

 

7. A car going 10 m/s hits a soft wall head on.  The front crunches up, and as a result the rest of the car comes to rest in about ½ meter. 

 

a) Approximately how long does it take for the car to come to rest?

 

The velocity changes by 10 m/s in ½ m.  But we need the time taken to stop.  Use d = vavet to get
½ m = (5 m/s)t.  Thus, t = 0.1 s.

 

b) What is the (negative) acceleration of the car as it comes to rest.

 

The acceleration is defined as (change in v)/(change in t) = (-10 m/s)/(0.1 s) = -100 m/s2.

 

8. The muzzle velocity of a pellet gun is 100 m/s. Neglecting air resistance, how high will the bullet travel in one second?

 

The bullet will not go 100 meters because it is not going 100 m/s for 1 second.  After 1 s the velocity has been reduced to 90 m/s.  Its average velocity is therefore 95 m/s, and the height after 1 s is 95 m.

 

9. A rocket initially at rest accelerates at 50 m/s2 for one minute.  Its final speed will be

 

(1) 50 m/s   (2) 500 m/s   (3) 3000 m/s   (4) 3600 m/s   (5) none of these

 

Velocity is acceleration times time.  Therefore v = (50 m/s2)(60 s) = 3000 m/s

 

10. Which one or more of the following are true for a given object?

a) It requires the same force to accelerate the object 1 m/s2 on both the moon and the earth.

b) The object has the same weight on the moon as it has on the earth.

c) The object has the same mass on the moon as it has on the earth.

 

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

 

Don’t forget that mass is everywhere the same.  Only the weight, which is the force of gravity, changes.

 

11. Which diagram implies the largest net force and which implies the smallest net force?

 

The net force for (1) is about 10 N, for (2) is about 7 N, for (3) is about 5 N, and for (4) is 8 N

 

12. A ball on a flat surface whirls in a circular path at the end of a cord.  We are looking down on the whirling ball at the instant the cord breaks.  Which path is the ball expected to follow after the string breaks?

 

 

Once the string breaks, there is no longer a force acting on the ball.  This means the ball must travel in a straight line.  The answer must be path (2)

 

 

 

13. An astronaut on another planet drops a 1-kg rock from rest.  The rock is observed to fall 2 m straight down in one second.  How much does the rock weigh on this planet?

 

From d = (1/2)at2, the acceleration of gravity on this planet is 4 m/s2.  The 1-kg mass weighs 4 N there.

 

14.A pair of tennis balls falls through the air from a tall building.  One ball is regular; the other is filled with lead pellets.  Air resistance just before they hit is ___.

 

(1) the same for both  (2) more for the regular ball   (3) more for the lead-filled ball

 

Since the lead filled ball has a higher weight and terminal velocity, it will have the greater air resistance.

 

15. Suppose a particle is being rapidly accelerated through space by a 10-N force.  Suddenly the particle encounters a second force of 10 N in the opposite direction from the first force.  As a result, the particle

 

(1) is brought to a rapid halt  (2) is brought to a gradual halt   (3) continues at the speed it had when it encountered the 2nd force  (4) tends to accelerate to a large velocity

 

When the second force is encountered, the net force becomes zero and the acceleration is zero

 

16. A man holds one end of a rope, passes the other end over a pulley mounted on the ceiling, grabs that other end and hangs suspended off the floor.  He weighs 500 N.  What is the tension in the rope?

 

Since the man holds two ends the tension is ½ the total weight.  The tension is 250 N.

 

17. Joe zips past Sue at a speed of 4/5 the velocity of light.  Each have identical clocks and meter sticks.  Which one or more of these are true, assuming that each person can in fact measure the other’s clock rate and meter stick ?

a) Sue sees Joe’s clock ticking slower than her own clock.

b) Joe sees Sue’s clock ticking slower than his own clock.

c) Joe sees Sue’s meter stick as longer than a meter.

 

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

 

18. Describe the two postulates on which the theory of relativity rests.

 

(1) The velocity of light is a constant in all frames of reference moving a constant velocity.

 

(2) The laws of physics are the same in all frames of reference moving a constant velocity.  There is no such thing as an absolute special frame (one that is at rest in the Universe).