Question

A block of mass 11.8 kg slides from rest down a frictionless 35.6° incline and is stopped by a strong spring with k = 3.11 x 10^4 N/m. The block slides 2.17 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest, how far has the spring been compressed?

Answer 1

x = 6.58 m

Step-by-step explanation:

For this exercise let's use the concept of conservation of mechanical energy. Let's look for energy at two points the highest and when the spring is compressed

Initial

Em₀ = U = m g and

Final

`E_(mf)` = ke = ½ k x2

As there is no friction the mechanical energy is conserved

Em₀ =
`E_(mf)`

m g y = ½ k x²

Let's use trigonometry to face height

sin θ = y / L

y = L sin θ

x = √ 2mg (L synth) / k

x = √ (2 11.8 9.8 2.17 sin35.6 / 3.11 104)

x = 6.58 m