A 2.0kg block of wood starts at rest and slides down a ramp. Its initial height is 12.0m. If the final velocity of the block is 13m/s, determine the energy of this system that has been turned into heat.

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To determine the energy of the system that has been turned into heat, we need to calculate the initial potential energy of the block, the final kinetic energy of the block, and then find the difference between them.

1. Calculate the initial potential energy (PE_initial) of the block:
The potential energy is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the height.
PE_initial = m * g * h
PE_initial = 2.0 kg * 9.8 m/s^2 * 12.0 m

2. Calculate the final kinetic energy (KE_final) of the block:
The kinetic energy is given by the formula KE = (1/2) * m * v^2, where m is the mass and v is the velocity.
KE_final = (1/2) * m * v^2
KE_final = (1/2) * 2.0 kg * (13 m/s)^2

3. Calculate the energy turned into heat:
The energy turned into heat is the difference between the initial potential energy and the final kinetic energy.
Energy turned into heat = PE_initial - KE_final

Substituting the values into the equations, we can now calculate:

PE_initial = 2.0 kg * 9.8 m/s^2 * 12.0 m
PE_initial = 235.2 J

KE_final = (1/2) * 2.0 kg * (13 m/s)^2
KE_final = 169 J

Energy turned into heat = PE_initial - KE_final
Energy turned into heat = 235.2 J - 169 J
Energy turned into heat = 66.2 J

Therefore, the energy of the system that has been turned into heat is 66.2 J.