Worksheet: Elasticity and Kinematics

In this worksheet, we will practice applying Hooke's law and elastic potential energy to situations that involve both kinematics and forces acting on springs.


An archer pulls the string of a bow back by 0.50 m, creating a tension of 150 N in the string. The mass of the arrow is 0.050 kg and the bowstring’s mass is negligible. What is the speed of the arrow after the bowstring is released and has returned to its equilibrium length? Assume that the force of the stretched bowstring on the arrow behaves like the force exerted by an extended spring and assume air resistance is negligible.


In the Hunger Games movie, Katniss Everdeen fires an arrow of mass 0.0200 kg from ground level to pierce an apple up on a stage. The spring constant of the bow is 330 N/m and she pulls the arrow back a distance of 0.550 m. The apple on the stage is 5.00 m higher than the launching point of the arrow.

At what speed does the arrow leave the bow?

At what speed does the arrow strike the apple?


In a competition, a contestant is firing watermelons with mass of 12 kg from a slingshot to hit targets down the field. The slingshot is pulled back 1.5 m and the watermelon is considered to be at ground level. The launch point is 0.30 m from the ground and the targets are 10 m horizontally away. Calculate the spring constant of the slingshot.


When a 3.0 kg block is pushed against a massless spring of force constant 4.5×10 N/m, the spring is compressed 8.0 cm. The block is released, and it slides 2.0 m (from the point at which it is released) across a horizontal surface before friction stops it. What is the coefficient of kinetic friction between the block and the surface?


Two 8.00 kg masses are connected to each other by a spring with a force constant of 25.0 N/m and a rest length of 1.00 m. The spring has been compressed to 0.900 m in length. The masses travel toward each other, and each mass moves at 0.500 m/s. What is the total energy in the system?


A toy gun uses a spring with a force constant of 350 N/m to propel a 12.0 g steel ball. The spring is compressed 10.0 cm and friction is negligible.

How much force is needed to compress the spring?

To what maximum height can the ball be shot?

At what angles above the horizontal may a child aim to hit a target 3.00 m away at the same height as the gun?

  • A 3 . 5 1 and 84.5
  • B 4 . 1 6 and 85.8
  • C 1 . 8 2 and 88.2
  • D 1 . 7 0 and 88.3
  • E 2 . 8 9 and 87.1

What is the gun’s maximum range on level ground?

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