Elastic potential energy Knowledge-Based Download PDF

Questions

1. 1.

   An ideal spring with an unstretched length of 0.40 m stores 2.0 J of elastic potential energy when stretched to a total length of 0.50 m. How much elastic potential energy is stored in the spring when its total length is increased to 0.60 m?

   • A) 8.0 J
   • B) 4.0 J
   • C) 6.0 J
   • D) 2.4 J
2. 2.

   A block of mass $m$ hangs in static equilibrium from the lower end of a vertical ideal spring, stretching it by an extension $\Delta L$. What is the elastic potential energy stored in the spring?

   • A) $2mg\Delta L$
   • B) $mg\Delta L$
   • C) $\frac{1}{2}mg\Delta L$
   • D) $\frac{1}{4}mg\Delta L$
3. 3.

   A small ball launched vertically upward by an ideal spring compressed by a distance $x$ reaches a maximum height $h$ above its launch position. Assuming all stored elastic potential energy is converted into gravitational potential energy, what maximum height will the ball reach if the spring is compressed by a distance $3x$ instead?

   • A) $9h$
   • B) $3h$
   • C) $6h$
   • D) $\sqrt{3}h$
4. 4.

   A 0.50 kg block resting on a frictionless horizontal surface is pushed against an ideal spring, compressing it by 0.10 m. If the spring constant is 800 N/m and the block is released from rest, what is its speed at the moment it loses contact with the spring?

   • A) 1.6 m/s
   • B) 2.0 m/s
   • C) 4.0 m/s
   • D) 8.0 m/s
5. 5.

   An ideal spring stores 36 J of elastic potential energy when held stretched by an applied force of 120 N. What is the extension of the spring from its equilibrium position?

   • A) 0.30 m
   • B) 0.60 m
   • C) 0.90 m
   • D) 1.20 m
6. 6.

   Two ideal springs, 1 and 2, have spring constants $k_1 = k$ and $k_2 = 2k$, respectively. If both springs are stretched by the same applied force within their elastic limits, what is the ratio of the elastic potential energy stored in spring 1 to that stored in spring 2, $\frac{U_1}{U_2}$?

   • A) $\frac{1}{2}$
   • B) 2
   • C) 4
   • D) $\frac{1}{4}$
7. 7.

   An ideal spring stores an elastic potential energy $E$ when it is stretched by a distance $x$ from its equilibrium position. How much additional work must be done by an external force to increase the stretch from $x$ to $2x$?

   • A) $E$
   • B) $3E$
   • C) $4E$
   • D) $5E$
8. 8.

   An ideal spring with a spring constant of 400 N/m is compressed by 0.15 m from its equilibrium position. How much elastic potential energy is stored in the spring?

   • A) 60 J
   • B) 30 J
   • C) 9.0 J
   • D) 4.5 J