A cleaver physics professor wants to create a situation where a block starts from rest at the top of a 31.0° inclined plane and encounters a spring at the bottom of the incline. The spring has a constant 3.4 kN/m and the block's mass is 33.0 kg. How far does the block travel before hitting the spring, if the spring was compressed 37 cm in it's initial collision?

Question

Physics

Araceli Duke

30 April, 10:36

A cleaver physics professor wants to create a situation where a block starts from rest at the top of a 31.0° inclined plane and encounters a spring at the bottom of the incline. The spring has a constant 3.4 kN/m and the block's mass is 33.0 kg. How far does the block travel before hitting the spring, if the spring was compressed 37 cm in it's initial collision?

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Answers (1)

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Adriana Buchanan · Answer 1

Let the length of inclined plane be L.

work done by gravity on the block

= force x length of path

= mg sinθ x L, m is mass of the block, θ is inclination of path

This in converted into potential energy of compressed spring

1/2 k x² = mgL sin31, k is force constant. x is compression

.5 x 3400 x. 37² = 33 x9.8 x sin31 L

L = 1.4

Length of incline = 1.4 m.