A 0.500 kg block covered with sandpaper is set down at the top of a piece of lum
ID: 1464608 • Letter: A
Question
A 0.500 kg block covered with sandpaper is set down at the top of a piece of lumber 2.00 m long. The lumber is inclined at 60.0 degree below the horizontal, and so the sandpaper slides down to the bottom. The coefficient of kinetic friction between the sandpaper and the lumber is 0.800. Calculate the work done on the block by friction. Calculate the work done on the block by gravity. Calculate the work done on the block by the normal force. Making sure you got the correct +/- signs on the work you calculated in parts a)-c), add them up to find the net work done by the three forces above. Assuming only these three forces acted on the block, use the Work-Energy Theorem (that is, W = 1/2 mv_final^2 - 1/2 mv_initial^2) to calculate the final speed of the block, just before it hits the floor.Explanation / Answer
Here ,
coefficient of friction , u = 0.8
mass of block , m= 0.5 Kg
length of lumber , L = 2 m
a)
work done by friction = -force * distance
work done by friction = - u*mg * cos(60) * L
work done by friction = - 0.8 * 0.5 * 9.8 * cos(60) * 2
work done by friction = -3.92 J
b)
work done by gravity = mg * L * sin(theta)
work done by gravity = 0.5 * 9.8 * 2 * sin(60)
work done by gravity = 8.49 J
c)
as the normal force is always perpendicular to the motion of block ,
the work done by normal force is zero
d)
net work done = sum of work by all three forces
net work done = -3.92 + 8.49 + 0
net work done = 4.67 J
the net work done on the block is 4.67 J
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