A box of textbooks of mass 25.2kg rests on a loading ramp that makes an angle ?
ID: 2277835 • Letter: A
Question
A box of textbooks of mass 25.2kg rests on a loading ramp that makes an angle ? with the horizontal. The coefficient of kinetic friction is 0.23 and the coefficient of static friction is 0.36.
A.As the angle ? is increased, find the minimum angle at which the box starts to slip. Express your answer using two significant figures.
B.At this angle, find the acceleration once the box has begun to move. Express your answer using two significant figures.
C.At this angle, how fast will the box be moving after it has slid a distance 5.0
Explanation / Answer
A) Force due to gravity in the plane of ramp = mg cos(alpha)
= 25.2*9.81*sin(alpha)
= 247.21 * sin(alpha)
Resisting frictional force = mu*N = mu * mg * cos(alpha)
= 0.36*25.2*9.81*cos(alpha)
= 88.99* cos(alpha)
Equating both for just slipping
tan(alpha) = 0.36
alpha = 20 degrees
B) When it will start moving, kinetic friction will act which is small and hence block will accelerate
ma = 247.21 * sin(20) - mu *25.2*9.81*cos(20) = 84.55 - (0.23)*232.3 = 31.07
a = 31.07/m = 31.07/25.2 = 1.2 m/sec^2
C) Using V^2 = U^2 +(2*a*S) U is zero in our case
V = sqrt(2 *1.2 * 5) = 3.5 m/sec
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