In: Physics
6.3: a factory worker pushes a 30 kg crate a distance of 4.5 m along a level floor at constant velocity by pushing horizontally on it. the coefficient of kinetic friction between the crate and the floor is 0.25.
Suppose the worker in exercise 6.3 pushes downward at an angleof 300 below the horizontal
(a) what magnitude of forcemust the worker apply to move the crate at constatnt velocity?
(b)how mach work is done on the crate by this force when the crate ispushed a distance of 4.5m?
(c) how mach work is done onthe crate by friction during this displacment?
(d) how much work isdone on the crate by the normal force? by gravity?
(e) what is thetotal work done on the crate?
a)
given velocity is constant accelaration will be zero
using the force values
Fcos - N = 0
Fsin + mg - N =
0
N = Fsin + mg
N value in the first equation
Fcos - ( Fsin +
mg ) = 0
Fcos - Fsin -
mg = 0
Fcos - Fsin = mg
F = mg / (cos -
sin)
F = 0.25 X 30 X 9.8 / (cos300 - 0.25 sin300)
F =73.5 / (0.5 - 0.25 X -0.866 )
F =73.5 / 0.7165
F = 102.58 N
this is the magnitude of force must the worker apply to move the
crate at constatnt velocity
b)
W = 102.58 X cos300 X 4.5
W = 102.58 X 0.5 X 4.5
W = 230.805 J
this is the work is done on the crate by this force when the crate ispushed a distance of 4.5m
c)
from the above result says that the work is done onthe crate by friction during this displacment 4.5 m
so the work is W = - 230.805 J
d)
work isdone on the crate by the normal force is zero joules
e)
the total work done on the crate is also zero joules
Work done by friction is also 345.5 joules.