A 20.0 -kg child is on a swing attached to ropes that are L=1.50 m long. Take the zero of the g

step 1 For this problem on the topic of energy conservation, we have a 20 kilogram child on a swing tha

A 20.0 -kg child is on a swing attached to ropes that are...

A 20.0 -kg child is on a swing attached to ropes that are $L=1.50 \mathrm{~m}$ long. Take the zero of the gravitational potential energy to be at the position of the child when the ropes are horizontal. a) Determine the child's gravitational potential energy when the child is at the lowest point of the circular trajectory b) Determine the child's gravitational potential energy when the ropes make an angle of $45.0^{\circ}$ relative to the vertical. c) Based on these results, which position has the higher potential energy?

A 20.0 -kg child is on a swing attached to ropes that are $L=1.50 \mathrm{~m}$ long. Take the zero of the gravitational potential energy to be at the position of the child when the ropes are horizontal.
a) Determine the child's gravitational potential energy when the child is at the lowest point of the circular trajectory
b) Determine the child's gravitational potential energy when the ropes make an angle of $45.0^{\circ}$ relative to the vertical.
c) Based on these results, which position has the higher potential energy?

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Key Concepts

Gravitational Potential Energy

This is the energy an object possesses due to its position in a gravitational field, often expressed as the product of mass, gravitational acceleration, and height (mgh). It is a fundamental concept in mechanics and is especially useful when analyzing energy changes in systems where the vertical displacement is involved.

Reference Level in Potential Energy Calculations

Setting a zero point for potential energy is essential because potential energy is defined relative to a chosen reference level. This concept emphasizes that only differences in potential energy have physical significance and that the chosen zero level can simplify problem-solving by making calculations more straightforward.

Vertical Displacement in Circular Motion

In problems involving pendulum motion or circular trajectories, the vertical height difference from a reference position can be determined using trigonometric relationships. By analyzing the geometry of the circular path—specifically using the length of the rope and the cosine of the angle—the change in vertical displacement can be accurately calculated, which directly affects the gravitational potential energy.

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