In the figure below, a small block is sent through point A with a speed of 9.5 m

Question

In the figure below, a small block is sent through point A with a speed of 9.5 m/s. Its path is without friction until it reaches the section of length L = 12 m, where the coefficient of kinetic friction is 0.70. The indicated heights are h1 = 7.4 m and h2 = 2.5 m.

(a) What is the speed of the block at point B? m/s

(b) What is the speed of the block at point C? m/s

(c) Does the block reach point D? If so, what is its speed there and if not, how far through the section of friction does it travel? in units of m or m/s?

Explanation / Answer

Here ,

a)

for the speed of block at B

using work energy theorum

0.5 * m * vA^2 + m * g * h1 = 0.5 * m * vB^2

0.5 * 9.5^2 + 9.8 * 7.4 = 0.5 * vB^2

vB = 15.34 m/s

the speed of the block at B is 15.34 m/s

b)

at the point C

using work energy theorum

0.5 * m * vA^2 + m * g * (h1 - h2) = 0.5 * m * vC^2

0.5 * 9.5^2 + 9.8 * (7.4 - 2.5 ) = 0.5 * vC^2

vC = 13.65 m/s

the speed of block at C is 13.65 m/s

c)

let the final speed is v

0.5 * m * v^2 - 0.5 * m * vc^2 = -u * mg * L

v^2 - 13.65^2 = - 0.7 * 9.8 * 2 * 12

v = 4.65 m/s

the velocity of block at D is 4.65 m/s

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