The ball has a mass of 340 g and is 1.2 m off the ground.If it currently has 18 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 10 N/kg.Ignore the effects of air resistance.Give your answer to 2 significant figures.You must include units in your answer.
Question
The ball has a mass of 340 g and is 1.2 m off the ground.If it currently has 18 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 10 N/kg.Ignore the effects of air resistance.Give your answer to 2 significant figures.You must include units in your answer.
Solution
First, we need to convert the mass of the ball from grams to kilograms because the standard unit of mass in physics is kilograms.
340 g = 0.34 kg
Next, we calculate the potential energy (PE) of the ball using the formula:
PE = mgh
where: m = mass of the ball = 0.34 kg g = gravitational field strength = 10 N/kg h = height off the ground = 1.2 m
PE = 0.34 kg * 10 N/kg * 1.2 m = 4.08 J
The ball also has 18 J of kinetic energy (KE) initially.
When the ball hits the ground, all of its potential energy will have been converted into kinetic energy (assuming no energy is lost due to air resistance). This is due to the conservation of energy principle, which states that energy cannot be created or destroyed, only transferred or converted from one form to another.
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 gained from falling.
Total KE = initial KE + PE Total KE = 18 J + 4.08 J = 22.08 J
Rounding to two significant figures, the total kinetic energy of the ball when it hits the ground is 22 J.
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