A 15 g lead bullet is tested by firing it into a fixed block of wood with a mass of 1.05 kg. The block and the embedded bullet together absorb all the heat generated. After thermal equilibrium has been reached, the system has a change in temperature measured as 0.020 oC. Estimate the entering speed of the bullet.

help :( do i equate them both?

ooh.. ok. thanks :)

Well, let's take a humorous approach to help you out!

Hmm... So, we have a bullet and a block of wood having a chill party together, huh? They're really heating things up! 😄

In order to determine the entering speed of the bullet, we can use the principle of conservation of energy. The heat generated must be equal to the kinetic energy of the bullet.

But how can we quantify this heat transfer? It's like trying to measure the temperature of my jokes... too hot to handle! 🔥

Now, let's get serious for a moment. The heat generated is given by the equation:

Q = mcΔT

Where:
Q = heat generated
m = mass of the system (bullet + block)
c = specific heat capacity of the system
ΔT = change in temperature

Since the change in temperature is given as 0.020 oC, we can plug in the values for mass and specific heat capacity and get:

Q = (15g + 1.05kg)(0.020 oC)

Now, let's convert grams to kilograms:

Q = (0.015kg + 1.05kg)(0.020 oC)

Calculating this will give you the heat generated, which equals the initial kinetic energy of the bullet.

But wait! We haven't accounted for the velocity of the bullet yet! Time to put the speedometer on the bullet party!

The kinetic energy of the bullet can be expressed as:

KE = 0.5mv^2

Where:
KE = kinetic energy
m = mass of the bullet
v = velocity of the bullet

Since the heat generated by the system equals the initial kinetic energy of the bullet, we equate Q to KE:

(0.015kg + 1.05kg)(0.020 oC) = 0.5 * 0.015kg * v^2

Now, just solve for v. But be careful, don't jump to conclusions too quickly. Take your time and calculate the velocity step by step.

I hope this helps you solve the problem while keeping a smile on your face! Remember, even when dealing with physics, a little humor never hurts! 😄

To estimate the entering speed of the bullet, we can use the principle of conservation of energy.

First, let's determine the amount of heat absorbed by the system. We know that the bullet and the wooden block have reached thermal equilibrium, which means they have the same final temperature.

The formula for heat is given by Q = mcΔT, where Q is the heat absorbed or released, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

In this case, the bullet and the block absorb the same amount of heat, so we can equate their heat values:

m_bullet * c_bullet * ΔT_bullet = m_block * c_block * ΔT_block

The specific heat capacity of lead is approximately 130 J/kg°C, and for wood, it is around 2.5 J/g°C.

Converting the mass of the bullet to kilograms: 15 g = 0.015 kg.

Substituting the values, we get:

0.015 kg * 130 J/kg°C * ΔT_bullet = 1.05 kg * 2.5 J/g°C * ΔT_block

Canceling the units, we are left with:

0.015 * 130 * ΔT_bullet = 1.05 * 2.5 * ΔT_block

Dividing both sides of the equation by ΔT_bullet and rearranging the equation, we have:

Entering speed of the bullet = 1.05 * 2.5 * ΔT_block / (0.015 * 130)

Finally, substitute the change in temperature ΔT_block with its value of 0.020 °C:

Entering speed of the bullet = 1.05 * 2.5 * 0.020 / (0.015 * 130)

Calculating this expression will give you an estimate of the entering speed of the bullet after it is fired into the block of wood.

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