Answer:
(a) Hence, the potential energy = 0.400 J.
(b) Hence the potential Energy = 0.225 J.
(c) Hence the potential energy = 0 J
Explanation:
Potential Energy; This is the energy of a body, by virtue of its position in the gravitational field. The unit of potential energy is Joules (J)
the potential energy stored in a spring is
Ep = 1/2ke²..................................... Equation 1
Where Ep = potential Energy, k = force constant, e = extension.
a.
When spring is stretched 4.00 cm, e = 4.00 cm = 4/100 = 0.04 m, and k = 500 N/m.
Substituting into equation 1
Ep = 1/2(500)(0.04)²
Ep = 0.4 J.
Hence, the potential energy = 0.400 J.
(b)
When the spring is compressed 3.00 cm, e = 3.00 cm = 3/100 = 0.03 m, and k = 500 N/m.
Substitute into equation 1,
Ep = 1/2(500)(0.03)²
Ep = 250(0.0009)
Ep = 0.225 J.
Hence the potential Energy = 0.225 J.
(c) When the spring is unstretched, e = 0 cm = 0 m and k = 500 N/m.
Substituting into equation 1
Ep = 1/2(500)(0)²
Ep = 250(0)
Ep = 0.
Hence the potential energy = 0 J
The potential energy of the spring for (a) is 0.4 J, For (b) is 0.225 J for (c) is 0 J.
The potential energy of a spring is the energy that is required to stretch the soring from its mean position.
The Formula of the potential energy of a stretched spring is,
P.E = ke²/2................... Equation 1
Where P.E = Potential energy of the stretched spring, k = spring constant or force constant of the spring, e = extension.
(a) From the question,
Given: k = 500 N/m, e = 4 cm = 0.04 m
Substitute these values into equation 1
P.E = 500(0.04²)/2
P.E = 0.4 J
(b) when e = 3 cm = 0.03 m
substitute into equation 1
P.E = 500(0.03²)/2
P.E = 0.225 J
(c) when e = 0 m
P.E = 500(0²)/2
P.E = 250(0)
P.E = 0 J
Hence, The potential energy of the spring for (a) is 0.4 J, For (b) is 0.225 J for (c) is 0 J
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