My problem is as follows "A 3 kg brick is dropped from a height of 1.0 m onto a nail which is vertically stuck in a plank of wood. If the nail doesn't move in much, how much heat is produced in the system when the brick hits and sticks onto the top of the nail." I know PE is 29.4J and this will convert to KE by the time it hits the nail but where does "heat" come into the picture?

Question

My problem is as follows "A 3 kg brick is dropped from a height of 1.0 m onto a nail which is vertically stuck in a plank of wood. If the nail doesn't move in much, how much heat is produced in the system when the brick hits and sticks onto the top of the nail." I know PE is 29.4J and this will convert to KE by the time it hits the nail but where does "heat" come into the picture?

Answer 1

The KE is converted to heat by friction on impact.

Answer 2

Thanks so much.

Answer 3

To find the amount of heat produced in the system when the brick hits and sticks onto the top of the nail, we need to understand the concept of energy conservation. When the brick falls from a height, it possesses potential energy (PE) due to its position relative to the ground.

As the brick falls, this potential energy is converted into kinetic energy (KE) - the energy associated with its motion. At the point of impact with the nail, the kinetic energy of the brick is entirely transferred into other forms of energy, primarily heat and sound.

The heat produced is a result of the impact between the brick and the nail. When the brick comes to a sudden stop, the kinetic energy is dissipated and converted into heat through deformation and friction. Some of this energy is also converted into sound energy due to the collision.

To calculate the amount of heat produced, we first need to determine the total energy converted from potential energy to kinetic energy. Given that the potential energy (PE) is 29.4J, this value also represents the initial kinetic energy (KE) just before the collision.

Next, we need to consider the conservation of energy. In an ideal situation, where there is no energy loss due to factors like air resistance, the total initial energy (PE) will be equal to the total final energy (KE + heat + sound):

PE = KE + heat + sound.

Since the problem states that the nail doesn't move much, we can assume that most of the energy will be converted into heat. Therefore, we can disregard the sound energy for simplicity. Hence:

PE = KE + heat.

Substituting the known value for potential energy (PE = 29.4J), we can solve for heat:

29.4J = KE + heat.

Since the brick comes to a stop upon sticking to the nail, all of its kinetic energy would be converted into heat. Therefore:

KE = heat.

Thus, the amount of heat produced in the system when the brick hits the nail and sticks onto it would be equivalent to the initial kinetic energy of the brick, which is 29.4J.