Sample Questions: Midterm 1

Physics 141 Sample questions: Midterm 1

1. A 10 kg crate sits 10 meters up an incline that makes an angle of 30 degrees with the horizontal direction.

a.) Assuming that there is a coefficient of kinetic friction k  0.25 , draw a free body diagram for the 10 kg mass. Identify the source of each force. b.) Find the friction force. c.) Find the work done by each of the forces as the mass slides to the bottom of the ramp. d.) Find the speed of the mass when it reaches the bottom of the incline.

2. The gravitron produces a sort of weightlessness by rotating about its central axis (represented by the vertical line on the right. The rider lays on the incline and is represented by the box on the slope. Assume that the incline is frictionless. At the location of the rider the velocity of the ride has speed v and is directed out of the page. The rider is executing circular motion at constant speed.

R = 5m

45˚ The Gravitron

a. Draw a free body diagram for the rider. Identify the source of each force. b. Using Newton’s Laws, construct the equations relating the forces and accelerations for a passenger of mass m. c. At what speed would the incline need to move so that the passenger would not slide up or down on the frictionless ramp? Express the result as a formula involving g and R. d. Find a formula for the normal force.

3. A 1000 kg auto moving north at 6 m/s skids into an icy, frictionless intersection and collides with a 2000 kg SUV skidding east at 4 m/s. The bumpers of the cars lock together and they skid off together. What is the final velocity of the wreckage?

4. Two identical particles collide and stick together as shown below. a. Find the total momentum. b. Find the final speed. c. Find the total initial and final kinetic energy d. How much energy is used to hold the particles together?

Initial Final

45o m1 = 1 g m2 = 1 g v1 = 10 m/s v2 = 5 m/s

5. Find an approximate expression for the force of gravity that holds a planet on an orbit about the Sun if the relationship between orbital period and orbital radius is T2 ~ r3.

6. Consider a ramp of length 1 m and angle of incline 30 degrees. A block of mass 5 kg is released from rest from the bottom of the ramp. At the bottom of the ramp is a spring with uncompressed length .1 m and spring constant k = 2x104 kgs-2.

0.05 m 1 m

a. If the block begins with the spring compressed to .05m, what is the initial energy of the block? b. What is the speed of the block when it reaches the top of the incline? Ignore friction. c. Draw free body diagrams for the block when it is at the bottom and the top of the ramp.

7. A 1 kg ball is released from a height of 1 m above a trampoline. After hitting the trampoline surface, the ball rebounds to a height of 2 m. About how much energy was added to the ball by the trampoline?

8. Show that a bullet fired from a gun with muzzle speed v and a bullet dropped from the same height reach the ground at the same time.

9. Compare the gravitational force and the acceleration due to gravity between you and the Earth, the Moon and you, and Jupiter and you. Feel free to comment on astrological bullshit.

10. Problem 3.65 1. Newton’s first law of motion states that

a. the total momentum of a system is conserved in the absence of any external forces. b. the force applied to an object is proportional to the acceleration it causes. c. an object moves in a straight line at constant speed or remains motionless unless acted upon by a force d. a robot may not harm, nor through inaction cause harm, to a human.

2. Consider the plot below of a particle’s 1-D acceleration with respect to time:

Which of the plots below shows the particle’s velocity as a function of time?

d) 3. Consider the case of a skydiver in free fall. Eventually, she reaches a constant velocity due to air resistance. Which of the following is then true?

a. The gravitational force is zero. b. The force due to air resistance is zero. c. The net force on the diver is zero. d. The gravitational force is greater than the air resistance force.

4. Which of the following requires the LEAST amount of work on the brakes of a car?

a. Slowing down from 150 kph to 100 kph. b. Slowing down from 100 kph to 50 kph. c. Slowing down from 50 kph to 0 kph. d. All the above require the same amount of work.

5. What are the SI units for momentum?

a. kg-m2/s b. kg-m/s c. kg-s/m d. N-J e. Liar! Momentum is unitless.

6. Captain Kirk boldly lands on a strange, new world in which the gravitational acceleration near the surface is half as large as on the Earth: |gp|= 1/2|g|. Neglecting air resistance, how would this affect the time it would take Kirk to fall a certain distance (naturally ripping his shirt in the process)?

a. tPlanet = tEarth. b. tPlanet = 2tEarth. c. tPlanet = (1/2)tEarth. d. tPlanet = √2tEarth. e. tPlanet = (1/√2)tEarth.

7. A mass is supported by two identical, massless wires as shown. Which wire has the smallest tension? A B a) Wire A b) Wire B c) Both wires have the same tension d) Not enough information is given to answer this problem. 8. Two hockey pucks glide across a frictionless, horizontal surface and collide elastically. Which of the following quantities is conserved in the collision?

a. Momentum b. Kinetic Energy c. Both of the above are conserved. d. None of the above is conserved.

9. The Sun has about 1 million times the mass of the Earth. About how many atoms comprise the Sun?

a. 10100 b. 1033 c. 10-3 d. 1057 e. 1039

10. Suppose the frictional force between a car’s tires and the road is responsible for the inward radial force that the car experiences as it makes a turn of radius R at constant speed v. Which of the following expressions would be true?

a. N = W. b. R = mv2/(mg). c. R = v2/m d. v = mg/N