A 1.50 kg snowball is fired from a cliff 12.5 m high. The snowball's initial velocity is 14.0

step 1 For this problem on the topic of conservation of energy, we are told that a 1 .5 kilogram snowba

A 1.50 kg snowball is fired from a cliff 12.5 m high. The...

A $1.50 \mathrm{~kg}$ snowball is fired from a cliff $12.5 \mathrm{~m}$ high. The snowball's initial velocity is $14.0 \mathrm{~m} / \mathrm{s}$, directed $41.0^{\circ}$ above the horizontal. (a) How much work is done on the snowball by the gravitational force during its flight to the flat ground below the cliff? (b) What is the change in the gravitational potential energy of the snowball-Earth system during the flight? (c) If that gravitational potential energy is taken to be zero at the height of the cliff, what is its value when the snowball reaches the ground?

A $1.50 \mathrm{~kg}$ snowball is fired from a cliff $12.5 \mathrm{~m}$ high. The snowball's initial velocity is $14.0 \mathrm{~m} / \mathrm{s}$, directed $41.0^{\circ}$ above the horizontal.
(a) How much work is done on the snowball by the gravitational force during its flight to the flat ground below the cliff? (b) What is the change in the gravitational potential energy of the snowball-Earth system during the flight? (c) If that gravitational potential energy is taken to be zero at the height of the cliff, what is its value when the snowball reaches the ground?

Key Concepts

Gravitational Potential Energy

Gravitational potential energy (GPE) is the energy possessed by an object due to its position in a gravitational field and is calculated as the product of the object's mass, the gravitational acceleration, and its height above a chosen reference level (i.e., GPE = mgh). This concept is essential in problems involving objects at different elevations because it allows us to quantify the energy associated with changes in height.

Work Done by the Gravitational Force

Work, in the context of a constant force like gravity, is defined as the product of the force and the displacement in the direction of the force. For gravity, which acts downward, the work done by gravity on an object moving vertically is equal to mgh (taking sign into account based on the direction of motion relative to the force). This work is directly related to the change in gravitational potential energy of the system.

Reference Level in Potential Energy Calculations

The selection of a reference level (or zero level) for potential energy is arbitrary and does not affect the physics of energy changes. Changing the zero point shifts the absolute values of potential energy but not the differences between energy states. This concept is particularly important when a problem explicitly defines the potential energy to be zero at a specific height, as it influences the computed values of potential energy but not the work done by gravity.

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