Sample Proficiency ExamPHYS 115

 

1. (25) A plane, diving at an angle of 53 degrees with respect to the vertical, releases a projectile at an altitude of 730 m. The projectile hits the ground 5.0 sec after being released.

 

 

 

 

 

 

   

A. What is the speed of the plane?

B. How far did the projectile travel horizontally during its flight?

C. What are the horizontal and vertical components of the projectile's velocity just before it hits the ground?

 

 

2. (25) A block of mass m₁ = 3.7 kg is placed on a frictionless inclined plane. This plane is angled 30 degrees above horizontal. The block is connected by an ideal, massless cord and frictionless, massless pulley to a second block of mass m₂ which hangs vertically near the end of the inclined plane.

 

 

 

 

 

 

 

A. What is the acceleration of each block?

B. What is the tension in the cord?

 

 

3. (25) A 40 kg slab rests on a frictionless floor. A 10 kg block rests on top of the slab. The coefficient of static friction between the block and the slab is 0.60 while the coefficient of kinetic friction is 0.40. The 10 kg block is acted on by a horizontal force of 100 N.What are the resulting accelerations of:

 

A. the block?

B.the slab?

 

 

 

 

4. (30) An unknown mass is attached to a pivot with an ideal string of length L. The mass is held at the same height as the pivot, with the string fully extended, and released. When the mass reaches the bottom of its swing, the string strikes a fixed peg located a distance d below the pivot point. Find the minimum distance d that will allow the mass to swing completely around the peg. (HINT: The string must not 'collapse' at the top of the arc around the peg.)

 

 

 

 

 

 

 

 

 

   

5. (20) A cart with mass 340 g moving on a frictionless linear air track at an initial speed of 1.2 m/s strikes a second cart of unknown mass which is initially at rest. The collision between the carts is elastic. After the collision, the first cart continues in its original direction at 0.66 m/s.

 

A. What is the mass of the second cart?

B. What is the speed of the second cart after the collision?

 

 

6. (25) Two 2.0 kg balls are attached to the ends of a thin, massless rod 50 cm long. The rod is free to rotate about a horizontal axis through its center. A 50 g putty ball moving at 3.0 m/s drops onto one of the balls and sticks to it.

 

 

 

 

 

 

 

A. What is the angular speed of the system just after the putty wad hits?

B. What is the ratio of the kinetic energy of the entire system after the collision to that of the putty wad just before the collision?

C. Through what angle will the system rotate before coming momentarily to rest (after which it will oscillate)?

 

 

7. (30) A vertical spring stretches 9.6 cm when a stationary 1.3 kg block is hung from its end. The block is displaced an additional 5.0 cm downward and released from rest so that it oscillates up and down.  

 

A. Calculate the spring constant.

B. Find the period of motion.

C. Find the frequency of the oscillation.

D. Find the amplitude of the oscillation.

E. What is the total energy of the system while it is oscillating?

F. What is the maximum speed of the block during its oscillation?

 

 

8. (20) Two identical cylindrical vessels with their bases at the same level each contain a liquid of density. The area of either base is A, but in one vessel the liquid height is h₁ and the other h₂. Find the work done by gravity in equalizing the levels when the two containers are connected.