Answer :
The work done by gravity= 163.17 J, change in kinetic energy=186.2J, the final velocity=93.67m/s
define kinetic energy ?
In physics, an object's kinetic energy is the energy it has as a result of its motion. It is defined as the amount of work required to accelerate a body of a given mass from rest to a certain velocity. The body retains its kinetic energy after gaining it during acceleration until its speed changes. The body does the same amount of work while slowing down from its current pace to rest. Formally, kinetic energy is any term in a system's Lagrangian that contains a time derivative.
a) work done by the gravity was
w=mg x (5.55) sin 17.5
=10x9.8x5.55x0.300
=543.9x0.300
=163.17 J
therefore the work done by gravity was 163.7 J
b)change in kinetic energy
Δu=(0.4)x(10)x(9.8)x(cos17.5)x(0.005)
=0.4x10x9.8xcos17.5x0.005
=0.4x10x9.8x0.95x0.005
Δu=186.2 J
c) speed of the cart after being pulled by the crate was
mass of the crate=10kg
initial speed=1.50
force=100 N
coeff. kinetic energy=0.4
distance=5.55m
frictional force N=mgcosФ
=0.4x10x9.8xcos17.5
=8.58
effective force = (100-8.58)
=91.42
acceleration=91.42/10
=9.142
the final velocity=u^2+2as
=1.5^2+2 (9.142)5
2.25 +2(45.71)
2.25+91.42
=93.67
therefore the final velocity=93.6m/s
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