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Answer:
The work done is 784 J and the PEg is 784 J.
Explanation:
In our case, we are to solve the work and potential energy of a mass that falls from a certain height. Here, we are going to discuss as well the relationship between work and potential energy.
For the formula, we will use:
1. W = ΔPEg
where
W is the work, unit is in N.m or Joules (J)
ΔPEg is the change of potential energy
2. W = F. s cos θ
where
F is the force, unit is in Newtons (N)
s is the distance, unit is in meter (m)
3. PE = mgh
where
m is the mass, unit is in kg
g is the acceleration due to gravity, 9.8 m/[tex]s^2[/tex]
h is the height or vertical position of an object, unit is in meter
For the given information
m = 20 kg
h = 400 cm = 4 m
W = ?
PEg = ?
Solving the problem
1. PEg = mgh
PEg = ((20 kg)(9.8 m/[tex]s^2[/tex])(4 m)
PEg = 784 J
2. Let us now introduce the relationship between work and potential energy. Let us prove the equality of this equation.
W = ΔPEg
Substitute the formula for work and potential energy.
F. s cos θ = mgΔh
Here, the force is the applied force or external force applied to lift an object with mass of 20 kg. The applied force is equal to the weight force which is:
F = mg substitute to the work - PEg equation, we have:
F. s cos θ = mgΔh
mg.s cos θ = mg Δh
The distance, s is the change of height of the 20 kg mass. Substituting this concept, we have:
mg.Δh cos θ = mg Δh
The angle between the direction of the force and gravitation is 180° since they are parallel to one another, therefore applying this concept to the equation, we have:
mg.Δh cos 180° = mg Δh
mg.Δh (1) = mg Δh
mg.Δh = mg Δh
Here, work is equivalent to gravitational potential energy.
Therefore, work is also equal to 784 J.
To learn more about potential energy and work, just click the links below:
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