I got the first one correct! A block with mass m = 14 kg rests on a frictionless

Question

I got the first one correct!

A block with mass m = 14 kg rests on a frictionless table and is accelerated by a spring with spring constant k = 5282 N/m after being compressed a distance x_1 = 0.45 m from the spring's unstretched length. The floor is frictionless except for a rough patch a distance d = 2.5 m long. For this rough path, the coefficient of friction is mu_K = 0.41. 1) How much work is done by the spring as it accelerates the block? 2) What is the speed of the block right after it leaves the spring? 3) How much work is done by friction as the block crosses the rough spot? 4) What is the speed of the block after it passes the rough spot?

Explanation / Answer

Here,

m = 14 Kg

k = 5282 N/m

x1 = 0.45 m

d =2.5 m

uk = 0.41

1)

work done by the spring = 0.5 * k * x^2

work done by the spring = 0.5 * 5282 * 0.45^2
work done by the spring = 534.8 J

2)
let the speed of block is v

using conservation of energy

534.8 = 0.5 * 14 * v^2

solving for v

v = 8.74 m/s

the speed of the block is 8.74 m/s

3)

work done by friction = - uk* m * g * d

work done by friction = -0.41 * 9.8 * 14 * 2.5

work done by friction = - 140.6 J

4)

let the final speed is v2

Using work energy theorum

0.5 * 14 * v2^2 = 534.8 - 140.6

solving for v2

v2 = 7.504 m/s

the speed of the block after passing rough spot is 7.504 m/s

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