The trampoline surface is extended by 0.50 m when the child lands and its spring constant is 4600 N/m.The mass of the child is 32 kg.When the trampoline returns to its original length it causes the child to gain 470 J of kinetic energy.Calculate the energy transferred to the surroundings.Energy(surroundings) = _____ J
Question
The trampoline surface is extended by 0.50 m when the child lands and its spring constant is 4600 N/m.The mass of the child is 32 kg.When the trampoline returns to its original length it causes the child to gain 470 J of kinetic energy.Calculate the energy transferred to the surroundings.Energy(surroundings) = _____ J
Solution 1
To solve this problem, we first need to calculate the total energy stored in the trampoline when it is extended. This can be done using the formula for the potential energy stored in a spring, which is:
PE = 0.5 * k * x^2
where k is the spring constant and x is the extension of the spring. Substituting the given values:
PE = 0.5 * 4600 N/m * (0.50 m)^2 = 575 J
Next, we know that when the trampoline returns to its original length, it transfers some of this energy to the child in the form of kinetic energy (KE), and the rest is transferred to the surroundings. The energy transferred to the child is given as 470 J.
Therefore, the energy transferred to the surroundings can be calculated by subtracting the energy gained by the child from the total energy stored in the trampoline:
Energy(surroundings) = PE - KE = 575 J - 470 J = 105 J
So, 105 Joules of energy is transferred to the surroundings.
Solution 2
To solve this problem, we first need to calculate the total energy stored in the trampoline when it is extended. This can be done using the formula for the potential energy stored in a spring, which is:
PE = 0.5 * k * x^2
where k is the spring constant and x is the extension of the spring. Substituting the given values:
PE = 0.5 * 4600 N/m * (0.50 m)^2 = 575 J
Next, we know that when the trampoline returns to its original length, it transfers some of this energy to the child in the form of kinetic energy (KE), and the rest is transferred to the surroundings. The energy transferred to the child is given as 470 J.
Therefore, the energy transferred to the surroundings can be calculated by subtracting the energy gained by the child from the total energy stored in the trampoline:
Energy(surroundings) = PE - KE = 575 J - 470 J = 105 J
So, 105 Joules of energy is transferred to the surroundings.
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