Question

A 2.4 kg block is launched along a level frictionless plane using a spring with constant 3000 N/m. When the spring is still compressed 10 cm = 0.10 m the block has a speed of 5 m/s. The block travels up a frictionless inclined plane to another level frictionless plane that is 0.76 m above the first. There is a spring at the end of the plane with constant 4000 N/m. How much kinetic energy does the block have when it has compressed the upper spring (k2 = 4000 N/m) 8.4 cm from its uncompressed length?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the block = m = 2.4 kg

Force constant of the spring on the lower plane = k₁ = 3000 N/m

Initial compression of the lower spring = d₁ = 10 cm = 0.1 m

Initial speed of the block = V₁ = 5 m/s

Height of the upper plane = h = 0.76 m

Force constant of the spring on the upper plane = k₂ = 4000 N/m

Compression of the upper spring = d₂ = 8.4 cm = 0.084 m

Kinetic energy of the block when the upper spring is compressed by 8.4 cm = E

By conservation of energy the total initial energy is equal to the total final energy.

KE = 12.99 J

Kinetic energy of the block when the upper spring is compressed by 8.4 cm = 12.99 J