a worker drives a .551 kg spike into a rail tie with a 2.55 kg sledgehammer. The hammer hits the spke with a speed of 62.1 m/s. if one fourth of the hammers kinetic energy is converted to the internal energy of the hammer and soike, how much does the total internal energy increase? answer in units of J.

Question

a worker drives a .551 kg spike into a rail tie with a 2.55 kg sledgehammer. The hammer hits the spke with a speed of 62.1 m/s. if one fourth of the hammers kinetic energy is converted to the internal energy of the hammer and soike, how much does the total internal energy increase? answer in units of J.

Answer 1

Compute the hammer's kinetic energy.

1/4 of that energy is converted to hammer and spike internal energy, or so they say.

The rest (3/4) supposedly does work on the rail tie.

Answer 2

To find the increase in total internal energy, we first need to calculate the initial kinetic energy of the sledgehammer.

The formula for kinetic energy is:

KE = 0.5 * mass * velocity^2

Plugging in the values, the initial kinetic energy of the sledgehammer is:

KE_sledgehammer = 0.5 * 2.55 kg * (62.1 m/s)^2

Next, we need to calculate the initial kinetic energy of the spike, which can be derived by using conservation of momentum. Since the spike and sledgehammer are initially at rest, the total momentum before the collision is zero. Therefore, the total momentum after the collision is also zero. We can express this as an equation:

(mass_sledgehammer * velocity_sledgehammer) + (mass_spike * velocity_spike) = 0

Since velocity_spike is the unknown, we can rearrange the equation as:

mass_sledgehammer * velocity_sledgehammer = -mass_spike * velocity_spike

Now we can substitute the given values into the equation:

2.55 kg * (62.1 m/s) = -0.551 kg * velocity_spike

Solving for velocity_spike, we get:

velocity_spike = (2.55 kg * 62.1 m/s) / -0.551 kg
velocity_spike ≈ -28.8 m/s

Note that velocity_spike is negative because it has the opposite direction of the sledgehammer's velocity.

Now we can calculate the initial kinetic energy of the spike:

KE_spike = 0.5 * 0.551 kg * (-28.8 m/s)^2

To find the increase in total internal energy, we need to determine one-quarter of the initial kinetic energy of the sledgehammer:

quarter_KE_sledgehammer = (1/4) * KE_sledgehammer

Similarly, we need to determine one-quarter of the initial kinetic energy of the spike:

quarter_KE_spike = (1/4) * KE_spike

Finally, we can calculate the increase in total internal energy as the sum of these two quantities:

increase_in_internal_energy = quarter_KE_sledgehammer + quarter_KE_spike

Now we can substitute the calculated values into the equation to get the final answer.