A pendulum swings in a vertical plane. At the bottom of the swing, the kinetic energy is \(8 \mathrm{~J}\) and the gravitational potential energy is 4 J. At the highest position of its swing, the kinetic and gravitational potential energies are a) kinetic energy \(=0 \mathrm{~J}\) and gravitational potential energy \(=4 \mathrm{~J}\) b) kinetic energy \(=12 \mathrm{~J}\) and gravitational potential energy \(=0 \mathrm{~J}\) c) kinetic energy \(=0 \mathrm{~J}\) and gravitational potential energy \(=12 \mathrm{~J}\) d) kinetic energy \(=4\) J and gravitational potential energy \(=8 \mathrm{~J}\) e) kinetic energy \(=8 \mathrm{~J}\) and gravitational potential energy \(=4\) J.

Step by step solution

01

Calculate the total mechanical energy at the bottom of the swing

Since energy is conserved, we can calculate the total mechanical energy at the bottom of the swing by adding the given kinetic energy and gravitational potential energy. In this case, KE = 8 J and PE = 4 J. Total Mechanical Energy (TME) = KE + PE = 8 J + 4 J = 12 J

02

Determine energies at the highest position of the swing

At the highest position of the swing, the pendulum is momentarily at rest, which means its kinetic energy is zero (KE = 0 J). When the kinetic energy is 0 J, all the energy must be potential energy, according to the conservation of mechanical energy. So, the gravitational potential energy at the highest position should be equal to the total mechanical energy we calculated in step 1. So, the energies at the highest position of the swing are: KE = 0 J PE = 12 J

03

Choose the correct answer

Now, we can compare our findings with the given options to choose the correct answer. Our KE and PE values match with option (c). The correct answer is (c) kinetic energy \(=0 \mathrm{~J}\) and gravitational potential energy \(=12 \mathrm{~J}\).

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