A 4 kg vase sits on a shelf at a height of 1.2 m. How much gravitational potential energy is added to the vase when it is lifted to a shelf of height 1.4 m?A.7.84 JB.47.0 JC.54.9 JD.31.2 J
Question
A 4 kg vase sits on a shelf at a height of 1.2 m. How much gravitational potential energy is added to the vase when it is lifted to a shelf of height 1.4 m?A.7.84 JB.47.0 JC.54.9 JD.31.2 J
Solution
The gravitational potential energy (PE) of an object can be calculated using the formula:
PE = mgh
where: m is the mass of the object (in kg), g is the acceleration due to gravity (approximated as 9.8 m/s² on the surface of the earth), and h is the height above the ground (in m).
The change in potential energy (ΔPE) when the vase is lifted from a height of 1.2 m to a height of 1.4 m can be calculated by subtracting the initial potential energy from the final potential energy:
ΔPE = PE_final - PE_initial
First, calculate the initial and final potential energies:
PE_initial = mgh = 4 kg * 9.8 m/s² * 1.2 m = 47.04 J PE_final = mgh = 4 kg * 9.8 m/s² * 1.4 m = 54.88 J
Then, calculate the change in potential energy:
ΔPE = PE_final - PE_initial = 54.88 J - 47.04 J = 7.84 J
So, the amount of gravitational potential energy added to the vase when it is lifted to a shelf of height 1.4 m is 7.84 J. Therefore, the correct answer is A.7.84 J.
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