Elastic potential energy Knowledge-Based Practice

Questions

1. 1.

   A mechanism extends an ideal spring with a spring constant of 600 N/m from its equilibrium length by 0.40 m in 4.0 s. What is the average power delivered to the spring to store this elastic potential energy?

   • A) 48 W
   • B) 24 W
   • C) 30 W
   • D) 12 W
2. 2.

   A light vertical spring with a spring constant of 800 N/m is compressed by 0.10 m from its equilibrium position. A 0.20 kg projectile placed on top of the compressed spring is released from rest; what is the maximum height the projectile reaches above its release position? (Assume negligible air resistance and take $g = 10\text{ m/s}^2$.)

   • A) 0.50 m
   • B) 1.0 m
   • C) 4.0 m
   • D) 2.0 m
3. 3.

   A 0.50 kg block on a frictionless horizontal surface is held against a compressed ideal spring with a spring constant of 200 N/m. If the spring is compressed by 0.10 m from its equilibrium position and then released from rest, what is the speed of the block at the moment it loses contact with the spring?

   • A) 0.50 m/s
   • B) 1.0 m/s
   • C) 1.4 m/s
   • D) 2.0 m/s
4. 4.

   An ideal spring stores 16 J of elastic potential energy when it is compressed by 0.20 m from its equilibrium position. What is the spring constant of the spring?

   • A) 80 N/m
   • B) 160 N/m
   • C) 800 N/m
   • D) 400 N/m
5. 5.

   An ideal spring is stretched by 0.25 m from its equilibrium position by an applied force of 40 N. What is the elastic potential energy stored in the spring?

   • A) 1.25 J
   • B) 5.0 J
   • C) 10 J
   • D) 160 J
6. 6.

   An ideal spring with a spring constant of 120 N/m is initially stretched by 0.10 m from its equilibrium position. How much additional work must be done on the spring to increase its extension to 0.30 m?

   • A) 2.4 J
   • B) 4.8 J
   • C) 5.4 J
   • D) 7.2 J
7. 7.

   An ideal spring with a spring constant of 250 N/m stores 5.0 J of elastic potential energy. What magnitude of tensile force is applied to hold the spring at this extension?

   • A) 50 N
   • B) 25 N
   • C) 10 N
   • D) 100 N
8. 8.

   Two springs with spring constants $k$ and $2k$ are stretched within their elastic limits by the same tensile force. What is the ratio of the elastic potential energy stored in the first spring to that stored in the second spring?

   • A) 1 : 4
   • B) 1 : 2
   • C) 2 : 1
   • D) 4 : 1
9. 9.

   An ideal spring stores an elastic potential energy $E$ when it is compressed by a distance $x$ from its equilibrium position. What is the elastic potential energy stored in the spring if its compression is increased to $3x$?

   • A) $3E$
   • B) $9E$
   • C) $6E$
   • D) $27E$
10. 10.

    A light spring with a spring constant of $400\text{ N/m}$ is stretched by $0.15\text{ m}$ from its unstretched length. What is the elastic potential energy stored in the spring?

    • A) $60\text{ J}$
    • B) $30\text{ J}$
    • C) $9.0\text{ J}$
    • D) $4.5\text{ J}$

Answers and step-by-step solutions appear after you finish the test.