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As shown in the figure below, a box of mass m = 27.0 kg is sliding along a horiz

ID: 2038807 • Letter: A

Question

As shown in the figure below, a box of mass m = 27.0 kg is sliding along a horizontal frictionless surface at a speed vi = 5.50 m/s when it encounters a ramp inclined at an angle of 9 = 25.8º. rough surface frictionless surface The coefficient of kinetic friction between the ramp and the box is u = 0.0704 and the box slides a distance d up the ramp before coming momentarily to rest. (a) Determine the distance (in m) the box slides up the ramp before coming momentarily to rest. (b) Determine which of the following statements is most correct about the box traveling up the ramp and coming momentarily to rest. O WNet = AKE W = -APE, Wnet = Wcons + Wnoncons O AE = Wroncons AE = AKE + APE O all of these

Explanation / Answer

Given,

m = 27 kg ; vi = 5.5 m/s ;theta = 25.8 deg ; u = 0.0704

a)The boc initially has KE which later gets conveted to PE and work done against the frictional forces.

From conservation of energy

1/2 m v^2 = m g d sin(theta) + u m g cos(theta) d

d = 0.5 v^2/g (sin(theta) + u cos(theta))

d = 0.5 x 5.5^2/9.81 (sin25.8 + 0.0 704cos25.8) = 3.1 m

Hence, d = 3.1 m

b)all the given looks correct

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