The ball has a mass of 2 kg and it is currently travelling at a velocity of 4 m/s upwards.It currently has 20 J of gravitational potential energy.How much will it have in total when it reaches its maximum height?Ignore the effects of air resistance.You must include units in your answer.
Question
The ball has a mass of 2 kg and it is currently travelling at a velocity of 4 m/s upwards.It currently has 20 J of gravitational potential energy.How much will it have in total when it reaches its maximum height?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 the total energy in a closed system remains constant. In this case, the closed system is the ball and the Earth. The total energy of the ball is the sum of its kinetic energy and its gravitational potential energy.
Step 1: Calculate the initial total energy of the ball. The kinetic energy (KE) of the ball can be calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the ball and v is its velocity. So, KE = 1/2 * 2 kg * (4 m/s)^2 = 16 Joules.
The initial gravitational potential energy (GPE) of the ball is given as 20 Joules.
So, the initial total energy of the ball is KE + GPE = 16 Joules + 20 Joules = 36 Joules.
Step 2: Calculate the total energy of the ball at its maximum height. According to the principle of conservation of energy, the total energy of the ball at its maximum height will be the same as its initial total energy, because no energy is added or lost in the system (we are ignoring air resistance).
So, the total energy of the ball at its maximum height will be 36 Joules.
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