A factory worker pushes a 30.1 kg crate a distance of 4.7 malong a level floor a
ID: 1348356 • Letter: A
Question
A factory worker pushes a 30.1 kg crate a distance of 4.7 malong a level floor at constant velocity by pushing downward at an angle of 31 below the horizontal. The coefficient of kinetic friction between the crate and floor is 0.25.
What magnitude of force must the worker apply to move the crate at constant velocity?
How much work is done on the crate by this force when the crate is pushed a distance of 4.7 m ?
How much work is done on the crate by friction during this displacement?
How much work is done by the normal force?
How much work is done by gravity?
What is the total work done on the crate?
Explanation / Answer
here,
mass of crate , m = 30.1 kg
distance , d = 4.7 kg
theta = 31 degree
uk = 0.25
(a)
let the force be F
Normal reaction , N = F*sin(theta) + m*g
N = 0.515 *F + 294.98
for constant velocity
F *cos(theta ) - uk*( N) = 0
F*cos(31) - 0.25 * ( 0.515 *F + 294.98 ) = 0
F = 101.24 N
the force needed is 101.24 N
(b)
work is done on the crate by this force when the crate is pushed a distance of 4.7 m , Wf = F*d*cos(theta)
Wf = 101.24 * 4.7*cos(31)
Wf = 407.86 J
work is done on the crate by this force when the crate is pushed a distance of 4.7 m is 407.86 J
(c)
work is done on the crate by friction during this displacement, Wff = - uk * ( 0.515 *F + 294.98 ) * d
Wff = - 466.16 J
work is done on the crate by friction during this displacement is - 466.16 J
(d)
work is done by the normal force is zero
(e)
work is done by gravity on the crate is zero
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