Mass of block= 20 kg moving to right, initial speed Vi=20 m/s , Height H=4m , ro

Question

Mass of block= 20 kg moving to right, initial speed Vi=20 m/s, Height H=4m, rough surface= 0.2 of L=2m located before the spring. Block is stopped by spring of force K=200 N/m

A- determine W done on the block by force of friction

B- determine compression of spring X

C- determine energy stored by spring when it is compressed the distance you obtained in part B

Explain

The diagram above (not drawn to scale) shows a block of mass m = 20 kg moving to the The height of the inclined is h = 4m. All surfaces are smooth except for a rough surface (p-O 2) of length the spring. The block is stopped by a spring of force constant k 200 N/m. right with an initial speed of vo-20ms. L = 2m located before 3 A) Determine the work done on the block by the force of friction. B) Use energy considerations to determine the compression of the spring X

Explanation / Answer

Here,

m = 20 Kg

vi = 20 m/s

H = 4 m

u = 0.2

L = 2 m

k = 200 N/m

a)

work done by the frictional force = - force * distance

work done by the frictional force = - u * m * g * L

work done by the frictional force = -0.2 * 20 * 9.8 * 2

work done by the frictional force = -78.4 J

b)

Using conservation of energy

0.5 * k * x^2 - work done by friction + m * g * H = 0.5 * m * vi^2

0.5 * 200 * x^2 + 78.4 + 20 * 9.8 * 4 = 0.5 * 20 * 20^2

solving for x

x = 5.601 m

the spring is compressed by 5.601 m

C)

energy stored in the spring = 0.5 k * x^2

energy stored in the spring = 0.5 * 200 * 5.601^2

energy stored in the spring = 3137.6 J

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