A box of textbooks of mass 24.8 kg rests on a loading ramp that makes an angle ?
ID: 1412154 • Letter: A
Question
A box of textbooks of mass 24.8 kg rests on a loading ramp that makes an angle ? with the horizontal. The coefficient of kinetic friction is 0.24 and the coefficient of static friction is 0.35.
As the angle ? is increased, find the minimum angle at which the box starts to slip. Express your answer using two significant figures.
At this angle, find the acceleration once the box has begun to move. Express your answer using two significant figures.
At this angle, how fast will the box be moving after it has slid a distance 5.5 m along the loading ramp? Express your answer using two significant figures.
Explanation / Answer
Given,
m = 24.8 kg ; uk = 0.24 ; us = 0.35
In order for the box to slide
mg sin(alpha) = us mg cos(alpha)
sin(alpha)/cos(alpha) = us mg/mg = us
tan(alpha) = us
alpha = tan^-1(us) = tan^-1(0.35) = 19.3 deg
Hence, alpha = 19.3 deg
The net force will be:
Fnet = W - Ff
Fnet = ma = mg sin(alpha) - uk mg cos(alpha)
a = g[sin(alpha) - uk cos(theta)]
a = 9.81(sin19.3 - 0.24 x cos19.3) = 1.02 m/s^2
Hence, a = 1.02 m/s^2
we know from eqn of motion
v^2 = u^2 + 2 a s
v = sqrt (0 + 2 x 1.02 x 5.5) = 3.35 m/s
Hence, v = 3.35 m/s
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