Question

A 5.0 kg box moving at 2.0 m/s on a horizontal, frictionless surface runs into a light horizontal spring of force constant 85 N/cm. Use the work-energy theorem to find the maximum compression of the spring.

Answer 1

x = 4.85 cm

Step-by-step explanation:

From work energy theorem when dealing with a spring in compression, we know that total work done is;

W_t = ½kx²

Where;

k is Force constant

x is max compression

Now, we know that this is also equal to the kinetic energy.

K.E = ½mv²

Thus;

½kx² = ½mv²

Making x the subject;

x = √(mv²/k)

We are given;

m = 5 kg

v = 2 m/s

k = 85 N/cm = 8500 N/m

Thus;

x = √(mv²/k)

x = √(5 × 2²/8500)

x = 0.0485 m

x = 4.85 cm