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A 5 kg block is placed near the top of a frictionless ramp, which makes an angle of 30o degrees to the horizontal. A distance d = 1.3 m away from the block is an unstretched spring with k = 3 × 103 N/m. The block slides down the ramp and compresses the spring.

Required:
Find the maximum compression of the spring.

Respuesta :

onyebuchinnaji

The maximum compression of the spring is 0.146 m.

Work Energy theorem

The work done by the block when it slides down the ramp will be converted to elastic potential energy of the spring.

W = U

Fd = U

where;

  • F is the horizontal component of the block weight

mgsin(θ) x d = ¹/₂kA²

[tex]A^2 = \frac{2mg sin(\theta)d}{k} \\\\A = \sqrt{\frac{2mg sin(\theta)d}{k}} \\\\A = \sqrt{\frac{2(5 \times 9.8) sin(30)\times 1.3}{3\times 10^3}}\\\\A = 0.146 \ m[/tex]

Thus, the maximum compression of the spring is 0.146 m.

Learn more about work energy theorem here: https://brainly.com/question/22236101

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