Physics 131 Test/Exam Problems: Energy

Physics 131 Test/Exam Problems: Energy

1)A vertical spring having a spring constant of k = 500 N/m is used to launch a 2 kg box straight up. If the compression of the spring from its equilibrium length is d = 50 cm prior to launch, what is the maximum height H above its initial position that the box will reach? (Assume that the spring is massless and returns to its equilibrium length after the launch). (e)

(a)1.15 m

(b)1.87 m

(d)2.73 m

(e)3.19 m

2)By what factor should the spring constant in the above problem be increased if we want the same height H to be reached by the box but we want the initial compression d of the spring to be 5 cm rather than 50 cm? (c)

(a)sqrt(10)

(b)10

3)Two objects have the same momentum, but have different masses. If KH and KL are the kinetic energies of the heavier and the lighter object respectively then: (a)

(a)KH < KL

(b)KH = KL

(c)KH > KL

4)A block sits at rest on a horizontal surface. It suddenly explodes into two pieces. A piece of mass 5 kg goes to the left and a piece of mass 20 kg goes to the right. The blocks each slide along the surface, then up a ramp. The speed of the 5 kg block is 8 m/s immediately after the explosion.

What is the speed v20 of the 20 kg block just after the explosion?(b)

(a)v20 = 0.50 m/s

(b)v20 = 2.00 m/s

(c)v20 = 3.00 m/s

(d)v20 = 4.00 m/s

(e)v20 = 8.00 m/s

5)What is the maximum height h reached by the 5 kg block? (b)

(a)h = 5.20 m

(b)h = 3.26 m

(c)h = 1.20 m

(d)h = 0.82 m

(e)h = 0.38 m

6)A skier with a mass of 50 kg starts from the top of a hill at height h above ground. The skier glides down the hill to point A where her velocity is vA = 20 m/s and continues up a second hill 8 meters high and back down the other side. Her entire trip up to point C is frictionless. At point C she begins stopping and comes to a complete stop 48 meters later at point D.

What is the height h of the hill? (c)

(a)h = 11.1 m

(b)h = 16.2 m

(c)h = 20.4 m

(d)h = 28.5 m

(e)h = 33.1 m

7)What is the speed vB of the skier when she reaches point B? (d)

(a)vB = 9.64 m/s

(b)vB = 11.2 m/s

(c)vB = 12.5 m/s

(d)vB = 15.6 m/s

(e)vB = 23.6 m/s

8)What is the magnitude of the average stopping force FCD from C to D?(b)

(a)FCD = 81.6 N

(b)FCD = 208 N

(c)FCD = 282 N

(d)FCD = 328 N

(e)FCD = 490 N

9)Two identical blocks are a distance h = 0.4 meters above the ground. Block 1 is dropped straight down, block 2 slides down a frictionless ramp of length L = 1 meter. Compare the velocity of block 1 just before it reaches the ground v1, with the velocity of block 2 just before it reaches the ground v2. (b)

(a)v1 > v2

(b)v1 = v2

(c)v1 < v2

10)Compare the amount of time t it takes each block to reach the ground. (c)

(a)t1 > t2

(b)t1 = t2

(c)t1 < t2

11)A block of mass M slides down a ramp of height h0 and collides with an identical block that is initially at rest. The two blocks stick together and slide up a different ramp, reaching a maximum height h1. All surfaces are frictionless. (e)

What is the height h1?

(a)h0

(b)2h0

(d)h0/2

(e)h0/4

12)This problem deals with the roller coaster Raging Bull at Six Flags Great America. In the first drop you fall essentially from rest a distance of 61 m. (a) What speed will you have in miles per hour when you reach the bottom of the drop? (1 m/s = 2.24 mph) Soon after you encounter a loop de loop as in the picture. (b) What Force does the track exert on the car at the top of the loop? Give your answer in Newtons. (Assume the car has a mass of 3500 kg, and that the loop de loop is a perfect circle of diameter 15 m). Disregard the friction of the track in all parts of this problem. (about 77 mph, 3.85 105 N))