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 from a flat bench raised by 1.0 m above the ground. The cube covers a horizontal distance of 4.0 m before landing on the ground. 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.

A spring-loaded door stopper is designed to absorb energy to prevent the door from hitting the wall. It has a spring constant of 250.0 N/m. To prevent damage from a particularly heavy door, the stopper needs to absorb 75.0 J of energy. How far will the spring in the stopper compress under this impact?

A fruit basket with a total mass of 3.0 kg is gently placed on a kitchen scale, compressing the scale’s spring by 2.0 mm, which accurately displays the basket's weight. If the same basket is accidentally dropped from a height of 0.50 m onto the scale, what maximum weight does the scale display at the moment of greatest compression?

Sophia is mountain climbing when she unfortunately slips and falls off a ledge. She is secured with a 20-m-long dynamic climbing rope that only begins to stretch after she has fallen 20.0 m below the ledge. Sophia’s mass is 60.0 kg, and the rope obeys Hooke's law, $F = -kx$, with k = 70.0 N/m. Ignoring air resistance and the mass of the rope, estimate the distance d below the ledge that Sophia’s harness will be when she is momentarily motionless. Assume Sophia can be treated as a point mass.

An adventure sports company is installing a safety net with a spring mechanism below a bungee jumping platform to provide an additional layer of safety. The net needs to be designed so that if a jumper's bungee cord were to fail at the lowest point of their jump, the spring in the safety net would decelerate the jumper to a stop with an acceleration no greater than 3g. Assuming the lowest point of the jump is at height $h$ above the safety net, calculate the spring constant k necessary for the safety mechanism. Let M be the mass of an average jumper.

A bowling ball of mass 5.0 kg is kept at the free end of a compressed spring (k = 62 N/m) installed at the bottom of a steep hill. The hill makes an angle of 35° with the horizontal at the bottom of the hill. Given that, the equilibrium length of the spring is 1.50 m and the compressed spring length is 0.60 m calculate how far up the hill the bowling ball will travel before coming to a stop if the spring is released. (Assume that friction is negligible.)

A spring-loaded boxing glove is installed at the foot of an inclined plane. The incline makes an angle of 37° with the horizontal. The spring-loaded boxing glove is compressed to a length of 0.70 m whereas its equilibrium length is 1.40 m. If the glove attached to the spring has a mass of 0.45 kg and the spring constant of the spring mechanism is k = 85 N/m, calculate how far up the incline the glove will travel before stopping if the spring-loaded mechanism is released. (Ignore friction)

A spherical ball of mass 2.5 kg is attached to one end of a spring. The other end of the spring is fixed at the foot of an inclined plane as shown in the figure. The incline makes an angle of 32° with the horizontal. The spring with an equilibrium length of 1.60 m is compressed to 0.80 m and then released. Afterward, the ball traveled up the incline and stopped just as it reached the spring's equilibrium position. If the coefficient of kinetic friction between the ball and the inclined surface is μ, calculate its value. (Assume that the spring constant k = 62 N/m.)

An apple, with a mass of 0.381 kg, is launched upwards by a vertically oriented, massless spring. The spring, which has a spring constant of 876 N/m, is compressed 0.161 meters from its equilibrium position and then released. Calculate the initial upward velocity of the apple at the moment it detaches from the spring, ignoring air resistance and other non-conservative forces.

A truck weighing around 1800 kg is moving on an even surface at an approximate velocity of about 100 km/h when it collides with a coiled spring and stops after covering about 3.0 m. Calculate the value for this particular coil's constant. Assume that no thermal energy is produced in this collision.

An engineer is testing a spring mechanism with spring constant k = 120 N/m. The spring is in horizontal orientation with a mass of 5.0 kg attached to its free end. The mass rests on the floor which can assumed to be frictionless. If the mass is pulled from the equilibrium position of the spring and the spring is stretched by an amount Δx = 1.4 m, what would be the system's total energy if the mass is set free?