Homework #6 1. A 3 kg block is on a horizontal frictionless plane. The tension i
ID: 1583851 • Letter: H
Question
Homework #6 1. A 3 kg block is on a horizontal frictionless plane. The tension in the string is 10 N. How much work is done on the block in moving it 20 m? Starting from rest what is the final speed? From problem 1, the coefficient of friction between the block and the plane is 0.3. What is the net work done and the final speed? 3. From problem 1, if the coefficient of kinetic friction between the block and the plane is 0.3 and the initial speed is 2 m/s, what is the net work done and the final speed. 4. A 2 kg ball is thrown from the top of a 5 m high building at a velocity of 10 m/s, 25 above the horizontal. What is the speed of the ball when it reaches the ground? 5. A 2 kg block is at the top of a 5 m long plane inclined at 35 to the horizontal. Starting from rest, find the speed of the block at the bottom of the planeExplanation / Answer
here,
1)
mass , m = 3 kg
tension , T = 10 N
theta = 30 degree
the work done , W = T * s * cos(theta)
W = 10 * 20 * cos(30) J
W = 173.2 J
let the final speed be v
using work energy theorm
0.5 * m * (v^2 - u^2) = W
0.5 * 3 * ( v^2 - 0) = 173.2
solving for v
v = 10.7 m/s
the final speed is 10.7 m/s
2)
the coefficient of friction , uk = 0.3
the net force , F = ( T * cos(theta) - uk * m * g * sin(theta))
F = ( 10 * cos(30) - 0.3 * 3 * 9.81 * sin(30)) N
F = 4.25 N
the net work done , W = F * s
W = 84.9 J
let the final speed be v
using work energy theorm
0.5 * m * (v^2 - u^2) = W
0.5 * 3 * ( v^2 - 0) = 84.9
solving for v
v = 7.5 m/s
the final speed is 7.5 m/s
3)
the coefficient of friction , uk = 0.3
the net force , F = ( T * cos(theta) - uk * m * g * sin(theta))
F = ( 10 * cos(30) - 0.3 * 3 * 9.81 * sin(30)) N
F = 4.25 N
the net work done , W = F * s
W = 84.9 J
initial speed , u = 2 m/s
let the final speed be v
using work energy theorm
0.5 * m * (v^2 - u^2) = W
0.5 * 3 * ( v^2 - 2^2) = 84.9
solving for v
v = 7.8 m/s
the final speed is 7.8 m/s
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