Physics Practice Problems PDF

Preview

Summary

Practice problems for exam one
Professor Zhe Fe...

Description

Physics 101

Exam I

1. The distance between two cities is 200 km. A car was traveling form one of them to another. The average speed on the first 120 km was 40 km/h, and on the remaining distance, the speed was 80 km/h. Find the average speed of the car for the whole trip. A) B) C) D) E)

70 km/h 65 km/h 60 km/h 55 km/h 50 km/h

Solution: a) Find time for each part of the trip:

;

;

b) Find the whole time of the trip:

c) Find average velocity:

.

2. What statement about instantaneous speed, velocity and acceleration is wrong? A) B) C) D) E)

An object can have a varying velocity if its speed is constant. An object can have a varying speed if its velocity is constant. An object can have zero velocity if its acceleration is nonzero. An object can have zero acceleration if its velocity is nonzero. An object can have nonzero velocity if its acceleration is zero.

Solution: Speed is equal to the magnitude of the velocity. So, if the direction of the velocity is changing and the magnitude is the same we have a varying velocity a constant speed. An example: a car moving with constant speed along curved pass. By definition, if an object has a constant velocity, then both the object's speed and its direction of motion are constant. Therefore, the object CANNOT have a varying speed if its velocity is constant.

Page 1 of 9

Physics 101

Exam I

3. If two vectors are given such that direction of vectors A) B) C) D) E)

and

, what can you say about the magnitude and

?

Same magnitude, but can be in any direction Same magnitude, but must be in the same direction Same magnitude, but must be in opposite directions Different magnitudes, but must be in the same direction Different magnitudes, but must be in opposite directions

Solution:

4. A sprinter accelerates from A) B) C) D) E)

to

in 2.0 s. What is his acceleration?

2.0 m/s2 3.0 m/s2 4.0 m/s2 5.0 m/s2 7.0 m/s2

Solution: The average acceleration of the sprinter is

.

5. A car moves at . Then it brakes with constant acceleration of 2.0 m/s2 and comes to rest. What distance covered the car while it brakes? A) B) C) D) E)

10 m 40 m 80 m 100 m 200 m

Solution:

;

6. The graph of position versus time for a car is given below. What can you say about the velocity of the car over time? A) B) C) D) E)

It speeds up all the time It slows down all the time It moves at constant velocity Sometimes it speeds up and sometimes it slows down Not really sure Page 2 of 9

Physics 101

Exam I

Solution: Velocity is equal to the slope of the graph of position versus time 7. A stone initially at rest falls down from a tower. How far will it fall during 1.0 s? A) B) C) D) E)

1.0 m 4.9 m 9.8 m 19.6 m 23.0 m

Solution:

;

8. A stone initially at rest falls down from a tower. What is its speed after1.0 s? A) B) C) D) E)

1.0 m/s 4.9 m /s 9.8 m/s 19.6 m/s 23.0 m/s

Solution:

9. A small cart is rolling at constant velocity on a flat track. It fires a ball straight up into the air as it moves. (Recall lecture demonstration.) After it is fired, what happens to the ball? A) B) C) D) E)

It falls behind the cart It falls in front of the cart It falls right back into the cart It depends on how fast the cart is moving It remains at rest

Solution: In the frame of reference of the cart, the ball only has a vertical component of velocity. So it goes up and comes back down. To a ground observer, both the cart and the ball have the same horizontal velocity, so the ball still returns into the cart.

Page 3 of 9

Physics 101

Exam I

10. A ball is fired at a speed of 20 m/s at an angle 30° above the horizontal. How long does it take to go up to the highest point? (Neglect air resistance.) A) B) C) D) E)

1s 2s 3s 4s 5s

Solution: Vertical component of velocity: At the highest point:

11. Find the acceleration of a car that travels at a constant speed the radius of 200 m. A) B) C) D) E)

around a curve with

1.0 m/s2 2.0 m/s2 3.0 m/s2 4.0 m/s2 5.0 m/s2

Solution:

12. A hockey puck slides on ice at constant velocity. What is the net force acting on the puck? A) B) C) D) E)

More than its weight Equal to its weight Less than its weight but more than zero Depends on the speed of the puck Zero

Solution: Page 4 of 9

Physics 101

Exam I

The puck is moving at a constant velocity, and therefore it is not accelerating. Thus, there must be no net force acting on the puck

13. From rest, we step on the gas of our car, providing a force F for 3 s, speeding it up to a final speed v. If the applied force were only 1/2 F, how long would it have to be applied to reach the same final speed? A) B) C) D) E)

6s 9s 12 s 15 s 24 s

Solution: In the first case, the acceleration acts over time t =3 s to give velocity v = at. In the second case, the force is half, therefore the acceleration is also half, so to achieve the same final speed, the time must be doubled.

14. Consider two identical blocks, one resting on a flat (horizontal) surface, and the other resting on an incline. For which case is the normal force greater? A) B) C) D) E)

Blocks resting on a flat surface Blocks resting on an incline Both the same (normal force: N = mg) Both the same (0 < N < mg) Both the same (N = 0)

Solution: In case A, we know that N = mg. In case B, due to the angle of the incline, N < mg. In fact, we can see that N = mg cos(ϴ), where ϴ is angle between the incline and horizontal plain.

15. A block of mass m rests on the floor of an elevator that is accelerating upward. What is the relationship between the force due to gravity and the normal force on the block? A) B) C) D) E)

N = 0 N < mg (but not zero) N = mg N > mg Depends on the size of the elevator

Solution: Page 5 of 9

Physics 101

Exam I

The block is accelerating upward, so it must have a net upward force. The forces on it are N (up) and mg (down), so N must be greater than mg in order to give the net upward force! F = N – mg = ma > 0; N > mg. 16. Find weight of a 2.00-kg rock. The rock is located in Ames. A) B) C) D) E)

2.0 N 2.0 kg 9.8 N 9.8 kg 19.6 N

Solution:

17. What is the maximum acceleration a car can undergo if the coefficient of static friction between the tires and the ground is 0.50? A) B) C) D) E)

19.6 m/s2 9.8 m/s2 7.8 m/s2 4.9 m/s2 2.5 m/s2

Solution: A free-body diagram for the accelerating car is shown. The car does not accelerate ve If

n o . The static frictional force is the accelerating force, and so e the maximum acceleration, then we need the maximum force, and so the static

frictional force would be its maximum value of

.

. Thus we have

18. Calculate the acceleration due to gravity at a distance of 2 Earth radii above the Earth’s surface (3 radii from the center of the Earth). A) B) C) D)

9.8 m/s2 4.9 m/s2 3.3 m/s2 1.1 m/s2 Page 6 of 9

Physics 101

Exam I

E) Zero Solution:

19. A roller coaster starts out from rest at the top of a hill of height 20 m. How fast is it going when it reaches the bottom? (Neglect friction and air resistance.) A) B) C) D) E)

20 m/s 15 m/s 10 m/s 8 m/s 5 m/s

Solution:

;

20. A ball is attached to a string and is made to move in circles. Find the work done by centripetal force to move the ball 1.0 m along the circle. The mass of the ball is 0.10 kg, and the radius of the circle is 1.0 m. A) B) C) D) E)

6.2 J 3.1 J 2.1 J 1.0 J zero

Solution: Work done by centripetal force is zero, because centripetal force is perpendicular to displacement.

21. The mass of the earth is 81 times the mass of the moon. The magnitude of the gravitational force of Earth on the Moon is __ times the magnitude of the gravitational force of the Moon on the Earth. A) B) C) D)

81 812 1 1/81 Page 7 of 9

Physics 101

Exam I

E) (1/81)2 Solution: These are Third Newton’s law forces; they are equal.

22. A spring has a spring stiffness constant, k, of stretched to store 8.0 J of potential energy? A) B) C) D) E)

. How much must this spring be

0.1m 0.2 m 0.3 m 0.4 m 0.5 m

Solution: The elastic potential energy is given by or compressing of the spring from its natural length.

where x is the distance of stretching

23. A system of particles is known to have a total kinetic energy of zero. What can you say about the total momentum of the system? A) B) C) D) E)

Momentum of the system is positive Momentum of the system is negative Momentum of the system is zero Momentum of the system could be positive or zero Momentum of the system could be positive, negative or zero

Solution: From definitions of linear momentum and kinetic energy (

and

) follows that momentum is zero if kinetic energy is zero.

24. A ball of mass, m1 = 2.0 kg has a horizontal velocity, of v1 = 5.0 m/s. The ball collides into a cart full of sand, as shown below. The cart has a mass, m2 = 6.0 kg and a horizontal velocity v2 = 1.0 m/s. The ball and the cart are moving towards each other. Find the velocity of the cart and the ball after the ball collides with the cart and gets stuck in the sand. A) B) C) D)

4.0 m/s 3.5 m/s 0.8 m/s 0.5 m/s 8 of 9

Physics 101

Exam I

E) 0.4 m/s

Solution:

Page 9 of 9...