Answer: -1,277 J
Explanation:
When no non-conservative forces are present, the total mechanical energy (sum of the kinetic energy and the potential energy) must be conserved.
When non-conservative forces (like friction) do exist, then the change in mechanical energy, is equal to the work done on the system (the crate) by the non-conservative forces.
So, we can write the following expression:
∆K + ∆U = WFNC
If the crate starts from rest, this means that the change in kinetic energy, is simply the kinetic energy at the bottom of the ramp:
∆K = ½ m v2= ½ . 30.5 kg . (2.35)2 m2= 84.2 J (1)
Regarding gravitational potential energy, if we take the bottom of the ramp as the zero reference level, we have:
∆U = 0- m.g.h = -m.g. h
In order to get the value of the height of the ramp h, we can apply the definition of the sinus of an angle:
sin θ = h/d, where d is the distance along the ramp = 7.7 m.
Replacing the values, and solving for h, we have:
h = 7.7 sin 36.2º = 4.55 m
So, replacing the value of h in the equation for ∆U:
∆U = 0 – (30.5 kg . 9.81 m/s2. 4.55 m) = -1,361 J (2)
Adding (1) and (2):
∆K + ∆U = 84.2J -1,361 J = -1,277 J
As we have already said, this value is equal to the work done by the non-conservative forces (friction in this case).
