Springs & Elastic Potential Energy Practice Problems

You obtain a massless spring from an old umbrella having a force constant, k = 1000 N/m. Out of sheer fun, you place the spring to rest vertically with one of its ends lying on a bench. Next, you release a block of mass 0.50 kg from a height of 1.5 m (measured from the spring's top end) directly above the spring. Determine the maximum compression that occurs on the spring.

A stainless steel spring with force constant k = 900 N/m has negligible mass. What compression will store 1.5 J of energy in the spring?

The force constant, k, for a spring with negligible mass fitted in a toy gun is 2500 N/m. How much compression is required to store 5.0 J of potential energy in the spring?

An experimental procedure for determining the force constant of a spring uses a compressed spring to shoot a 50 g cube at 40 degrees above the horizontal. A spring compressed by 25 cm projects the cube to a flat bench raised by 1.0 m above the launch point. The cube covers a horizontal distance of 4.0 m before landing on the bench. Determine the spring's force constant.

A Hooke's cord stretched to a distance d stores 3.0 J of energy. Determine the energy stored when the cord has a 5d stretching.

An 80 g cast iron block is shot up a clean and dry cast iron incline using a compressed spring located at the lower end of the incline. The incline slopes at an angle of 20°, and the spring force constant is 20 N/m. Take dry and clean cast iron-cast iron kinetic friction coefficient to be 0.15. When the spring is compressed by 15 cm, determine how long up the incline the block goes using work and energy.

A friction experiment involves launching objects up an incline from a compressed spring. The objects slide up and down a 40 degrees incline. An 80 g cast iron block is shot up a frictionless lubricated cast iron incline using a spring compressed by 150 mm. Use work and energy to determine the maximum height attained by the block above the starting point. Take the spring force constant as 80N/m.

Students in an interactive lesson compress a spring and use it to fire blocks, each weighing 500g, up a 1.5 m high frictionless incline onto a bench. If a spring with a force constant of 650 N/m is compressed by 50 cm, determine the speed of the block when it arrives at the bench.

A 25 kg crate is released from up an incline that makes 50° with the horizontal, such that it slides a distance of 3.5 m before striking a spring. The force constant of the spring is 320 N/m. Calculate the greatest compression that occurs on the spring.

Elastic cords are used to store and release energy. The stretching of a cord is determined by the design of the equipment. One equipment design allows a maximum stretching of 5.2 cm, while another allows a maximum stretching of 8.2 cm. Both types of equipment are fitted with the same type of cord, having a force constant of 25 N/cm. Calculate the difference in the greatest energy stored by the cords in the two equipment designs.

A lab bench has two sections: The first section is frictionless while the second section has a kinetic friction coefficient of 0.20 between an experimental block and the bench. A 4.20 kg block is launched on the frictionless section using a compressed piston whose spring constant is 150 N/m. If the piston is pushed (compressed) by 25cm to launch the block, calculate the length covered by the block on the rough surface before it goes to rest. Use the work-energy theorem.

A trolley moves on a rail at a processing plant. A loaded trolley weighs 8500 kg. The braking system of the trolley uses a hook to stretch elastic cords. If the force constant of the braking cord is 47 kN/m and the cord is stretched by 8 m to stop a trolley, calculate the trolley's speed before braking.

Elastic cords can be coupled to achieve a desired force constant. A single cord stretched by 200 mm (like a slingshot) launches a cube at 0.89 m/s through a frictionless bench. Three cords (identical to the first one) connected, as shown, are used to launch the same cube at the same stretching of 200 mm. Determine the cube's speed when launched from the combined cords.

You and your colleague live on opposite sides of a hill. You are located 8.5 m below the peak of the hill, while the colleague is located 12 m below the hill's peak on the opposite side. Using your physics knowledge, you built a track and a carriage that moves between your place and the colleague's place. The launching system uses an elastic cord and a handle that allows maximum stretching of 3.0 m. The maximum mass of the carriage is 500 kg, and the cord has a 15% greater spring constant than the minimum constant required to push the carriage above the hill for safety reasons. Find the maximum speed when a 420 kg carriage is launched at full stretching of the cord.