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A 2.1 ❝ 103-kg car starts from rest at the top of a 4.8-m-long driveway that...

A 2.1 ❝ 103-kg car starts from rest at the top of a 4.8-m-long driveway that is inclined at 23° with the horizontal. If an average friction force of 4.0 ❝ 103 N impedes the motion, find the speed of the car at the bottom of the driveway.

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Answer #1

According to the Conservation of Energy and Work:

Ui - W(friction) = Kf, U = mgdsin(theta), W(friction) = F(friction)d, and K = 0.5mv^2

Given that the mass of the car m is 2.1 * 10^3 kg, the length of the driveway d is 4.8 m, the angle of elevation theta is 23 degrees, and the force of friction F(friction) is 4.0 * 10^3 N,

mgdsin(theta) - F(friction)d = 0.5mv^2

v = sqrt[2(mgdsin(theta) - F(friction)d)/m]

v = sqrt[2(2.1*10^3*9.8*4.8*sin(23) - 4*10^3*4.8) / 4*10^3]

v = 3.1143


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