5. Outside the rear of a moving truck, a 35.0-kg box sits on 20.0 metal ramp. Su

Question

5. Outside the rear of a moving truck, a 35.0-kg box sits on 20.0 metal ramp. Suppose that the crate is given an initial downhill speed Vo a. If the coefficient of kinetic friction is 0.250, find the magnitude and direction of the box's acceleration. Over time, does the box speed up or slow down? box Vo A. 0.52 m/s downhill B. 0.78 m/s downhill C. 1.0 m/s downhill D. 1.3 m/s downhil E. 1.6 m/s downhill b. If the coefficient of kinetic friction is 0.500, find the magnitude and direction of the box's acceleration. Over time, does the box speed up or slow down? A. 0.52 m/s uphill B. 0.78 m/s uphill C. 10 m/s uphill D. 1.3 m/s uphill E. 16 m/s uphill c. Find the value of the coefficient of kinetic friction that will cause the crate to descend the ramp at a constant speed. A. 0.272 B. 0.303 C. 0.364 D. 0.426 E. 0.487 NQ Know : qyca, sind"4x.auosa sind-

Explanation / Answer

(a)

gravitational force component Fg = m*g*sintheta = 35*9.8*sin20 = 117.31 N down hill

frictional force fk = uk*m*g*costheta = 0.25*35*9.8*cos20 = 80.6 N up hill

Fg > fk

the acceleratio is down wards

Fnet = m*a

Fg - fk = m*a

m*a = m*g*sinthea - uk*m*g*costheta

a = g*(sintheta - uk*costheta)

a = 9.8*(sin20-(0.25*cos20))

a = 1.0 m/s^2 downhill

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(b)

a = g*(sintheta - uk*costheta)

a = 9.8*(sin20-(0.5*cos20))

a = -1.3 m/s^2

acceleration a = 1.3 m/s^2 up hill

OPTION (D)

======================

(c)

at constant speed acceleration a = 0

9.8*(sin20-(uk*cos20)) = 0

uk = 0.364

OPTION ( C )

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