A box is sliding up an indine that makes ar now far does the box travel along th

Question

A box is sliding up an indine that makes ar now far does the box travel along the indine bofore coming to rest respedt to the horicontal, The coefficient of kinetic friction betmeen the box and the surface of the indline is 01 The initial spend of the at the bottom of the indine is 2 Setion 41 spheres are located at the cormers of an equlateral triangle. Each side of the triangle has a legth of 3.80 m.T of the spheres have a mass of 3.20 kg each. The thlrd sphere(m nown) i eleased trom rest. the gravitational forces that the spheres exert on each other, what is the magnitude of the initial acceleration of the third sphere? m/s2 Secion 41 the floor is -037.etermine the magnitude and direction(reative to the axis) of the accleration of the crate direction Additional M

Explanation / Answer

1) Work Energy Theorem,

KE = Final PE + Energy Lost by friction

W = Force Times Distance

F = uFn

h = d*sin(angle)

The normal force on an incline is m*g*(cos(angle))

0.5*m*v^2 = m*g*h + u*m*g*(cos(angle))*d

0.5*m*v^2 = m*g*d*(sin(angle)) + u*m*g*(cos(angle))*d

0.5*(2.7)^2 = 9.8 * d * sin(13) + 0.180 * 9.8 * cos(13) * d

0.5*7.29 = 9.8 * d * ( sin(13) + 0.180 * cos(13) )

3.645 = 9.8 * d * (0.225 + (0.180 * 0.974))

3.645 = 9.8 * d * 0.40

d = 3.645 / 3.92

d = 0.93 m

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