2.) Pounding a nail into wood makes the nail warmer. Consider a 5-g steel nail 6 cm long and a hammer that exerts an average force of 500 N on the nail when it is being driven into a piece of wood. The nail becomes hotter. Show that the increase in the nail's temperature is 13.3oC. (Assume the specific heat capacity of steel is 450 J/kg*oC.)
I used the formula Q = cm(change in temp)
to get (Q being quantity of heat):
Q = 450J/kg(5g)13.3oC
I'm not sure where the 500N or 6cm come in.
Thanks so much! Now it makes sense. I still have a question, though. Why did you change the gm to kg? I wanted to know so that I would know when to convert. Thank you - Mary :-)
Well, it sounds like the nail had a heated encounter with the hammer! Let's get to the bottom of this.
First, we need to calculate the work done on the nail by the hammer. Work is defined as the force applied multiplied by the distance traveled. In this case, the force of 500 N is applied over a distance of 6 cm (or 0.06 meters), so the work done is given by:
Work = Force x Distance
Work = 500 N x 0.06 m
Work = 30 Joules
Since the work done is equal to the change in the nail's internal energy and there is no change in the nail's kinetic energy or potential energy, this work done results in an increase in the nail's temperature.
Now, we can use the specific heat capacity formula you mentioned to find the change in temperature of the nail. The formula is:
Q = m x c x ΔT
Q represents the heat transferred, m is the mass of the nail, c is the specific heat capacity of steel, and ΔT is the change in temperature.
Here, we need to use Q as the work done on the nail, which is 30 Joules. The mass of the nail is given as 5 grams (or 0.005 kg), and the specific heat capacity of steel is 450 J/(kg·°C). We plug in these values to solve for ΔT:
30 J = (0.005 kg) x (450 J/(kg·°C)) x ΔT
Now, we can solve for ΔT:
ΔT = 30 J / (0.005 kg x 450 J/(kg·°C))
ΔT ≈ 13.3°C
So, the increase in the nail's temperature is approximately 13.3°C.
I hope this explanation nailed it!
To calculate the increase in temperature of the nail when it is being pounded into the wood, you need to consider the work done on the nail and then convert it into heat. Here's how you can calculate it:
1. Start by calculating the work done on the nail. Work is defined as the force applied multiplied by the distance over which it is applied. In this case, the force applied is 500 N (given), and the distance is 6 cm (given).
Work = Force * Distance
Work = 500 N * 6 cm
Note: It is important to convert cm to m before calculating the work, as the SI unit of work is joules (J). 1 cm = 0.01 m.
Work = 500 N * 0.06 m
2. Next, convert the mass of the nail from grams to kilograms. The nail's mass is given as 5 g.
Mass = 5 g = 0.005 kg (since 1 kg = 1000 g)
3. Now, calculate the quantity of heat (Q) generated using the formula Q = mcΔT, where:
- Q represents the quantity of heat transferred
- m is the mass of the nail
- c is the specific heat capacity of steel
- ΔT represents the change in temperature
Q = mcΔT
Q = (0.005 kg)(450 J/kg*°C)(ΔT)
4. Since we are trying to find ΔT or the increase in temperature, we need to rearrange the equation:
ΔT = Q / (mc)
5. Now substitute the values:
ΔT = Work / (mc)
Note: The work done is equal to the quantity of heat transferred, as it is an energy transfer from mechanical work to heat due to pounding the nail.
ΔT = (500 N * 0.06 m) / (0.005 kg * 450 J/kg*°C)
6. Simplify the equation to find ΔT:
ΔT = (30 N·m) / (0.00225 J/°C)
ΔT = 1333.33 °C
Therefore, the increase in the nail's temperature is approximately 1333.33 °C.
It appears there was an error in your calculation. You seem to have multiplied the mass (5g) directly by the change in temperature (13.3°C), instead of multiplying the mass by the specific heat capacity (450 J/kg*°C), and then multiplying that by the change in temperature.
Force x distance = Work, and most of that work ends up as heat in the nail. (Actually, the wood heats up also, but they want you to neglect that because the heat does not travel far into the wood right away, although eventually it does).
Your equation for Q is not correct. They want you to compute Q from the force and nail length, and then use the heat capacity C o get the temperature change.
Q = 500 N x 0.06 m = 30 J
temperaure rise = Q/(M C)
= 30 J/[(.005kg)*(450J/kg C)]= __ C