The ball has a mass of 1.9 kg and is 2 m off the ground.If it currently has 30 J of kinetic energy, what will be the total amount of kinetic energy stored in the ball the moment it hits the ground?Gravitational field strength on Earth is 9.8 N/kg.Ignore the effects of air resistance.You must include units in your answer.
Question
The ball has a mass of 1.9 kg and is 2 m off the ground.If it currently has 30 J of kinetic energy, what will be the total amount of kinetic energy stored in the ball the moment it hits the ground?Gravitational field strength on Earth is 9.8 N/kg.Ignore the effects of air resistance.You must include units in your answer.
Solution
To solve this problem, we need to understand the principle of conservation of energy. This principle states that energy cannot be created or destroyed, only transferred or converted from one form to another.
In this case, the ball has two types of energy: kinetic energy (due to its motion) and potential energy (due to its height above the ground).
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First, let's calculate the potential energy (PE) of the ball when it is 2 m off the ground. The formula for potential energy is PE = mgh, where m is the mass, g is the gravitational field strength, and h is the height.
PE = (1.9 kg) * (9.8 N/kg) * (2 m) = 37.24 Joules
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The ball also has 30 J of kinetic energy (KE) initially.
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When the ball hits the ground, all of its potential energy will have been converted into kinetic energy (since it no longer has any height, its potential energy is 0).
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Therefore, the total kinetic energy of the ball when it hits the ground will be the sum of its initial kinetic energy and the potential energy it had due to its height.
Total KE = initial KE + PE Total KE = 30 J + 37.24 J = 67.24 Joules
So, the total amount of kinetic energy stored in the ball the moment it hits the ground will be 67.24 Joules.
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