Hooke's law and Elastic Potential Energy

A trampoline has a spring constant of 3430 N/m. How far will the trampoline sink when a 70 kg person steps on it?

0.2 m

A spring is compressed 0.035 m inside a dart gun. The spring constant (k) is 500 N/m. How much energy is stored in the spring?

0.31 Joules

A 5 kg ball is dropped from a height of 3 meters onto a vertical spring. The spring constant is 800 N/m. How far will the spring compress?

0.61 m

A vertical spring with a spring constant of 900 N/m has been compressed 0.8 meter. The spring is used to launch a 2 kg ball straight up into the air. How high will the ball go?

14.7 m

An archer used 2,000 J of energy to stretch a bow string 0.15 m. What is the spring constant (k) of the bow string?

180,000 N/m

If the force to stretch a spring is given as F = (100 N/m)x, then what is the potential energy of the spring if it is stretched 2 meters from rest?

200 Joules

2. What is the potential energy of a spring if the spring constant is 25.0 N/m and it is compressed to .5 m past its resting position?

3.125 Joules

A spring with a spring constant of 400 N/m has a mass hung on it so that it stretches 0.08 m. Calculate how much mass the spring is supporting.

3.2 Kg

A spring is stretched 0.06 m when a mass of 0.2 kg is hung on it. Calculate the spring constant of this spring.

33.3N/m

It takes a force of 20 Newtons to hold a spring stretched to a distance of 0.40 m. What is the elastic potential energy of the spring at this position?

4 Joules

A compressed spring has 20,000 J of energy stored in it. The spring constant (k) is 1,500 N/m. How far was the spring compressed?

5.16 m

A spring is stretched 0.2 meters. The spring constant (k) of the spring is 2500 N/m. How much energy is stored in the spring?

50 Joules

The force that is applied to the spring to stretch or compress it.

Applied force (F)

The distance (measured in meters) the spring stretches or compresses from its normal state or equilibrium. Displacement includes direction, because it is a VECTOR.

Displacement (x)

Formula for Elastic Potential Energy

E= 1/2 kx^2

F=kx where F is force, K is the constant of the spring, and X is the extension

Formula for Hooke's Law.

rigid spring, like the one on your car or on a trampoline

Large spring constant

Unit for force

Newtons

loose spring, like a slinky or the alien popper

Small spring constant

any elastic object able to store energy (spring, rubber band, popper, slingshot...)

Spring

Newtons/m, because it describes the force needed to stretch/compress the spring by a meter.

Spring constant is measured in _____

the extension of a spring within it's limits of elasticity, is directly proportional to the force applied.

State Hooke's Law using words.

stored energy, caused by the deformation of an object.

elastic potential energy (EPE)

Unit for displacement

meters

force applied (N) / extension (M) = constant (Nm)

spring constant