Hammering a nail into wood makes it get hotter. Consider a 5-g long, 5-gauge steel nail and a hammer that exerts an average force of 500 N on the nail when it is introduced to a piece of wood. The nail gets warmer each time. Demonstrate that the increase in the temperature of the nail is 13.3 ° C. (Suppose the specific heat of the steel is 450 J / kg * ° C)
heat=mass*specific heat*changintemp
but heat=force*distance
and you set them equal, solve for change in temp.
However, the distance the nail traveled is not specified. So it can't be worked. Wondering if you are in a class without a qualified teacher...or you are mistyping the questions.
To demonstrate that the increase in temperature of the nail is 13.3 °C, we can use the formula:
ΔT = (Q / (m * c))
where:
ΔT = change in temperature
Q = heat energy gained or lost
m = mass of the object
c = specific heat capacity of the object
In this case, let's calculate the heat energy gained by the nail when it is hammered, and then use the given mass and specific heat capacity to find the change in temperature.
We can calculate the heat energy gained using the formula:
Q = F * d
where:
Q = heat energy gained
F = force applied
d = distance over which the force is applied
Given:
Force applied (F) = 500 N
Distance over which the force is applied (d) = unknown
Now, we need to find the distance (d) over which the force is applied, which will allow us to calculate the heat energy gained (Q).
To find the distance (d), let's use the following information:
Mass of the nail (m) = 5 g = 0.005 kg
Gauge of the nail = 5-gauge (which provides information about the diameter of the nail)
For nails, the gauge number can be converted into diameter using the formula:
d = 0.127 * (92^((36 - Gauge)/39))
where:
d = diameter of the nail in inches
Gauge = gauge number
Let's calculate the diameter of the nail using the given gauge:
d = 0.127 * (92^((36 - 5)/39))
≈ 0.18 inches
We will assume that the entire length of the nail is hammered into the wood. Therefore, the distance over which the force is applied is equal to the diameter of the nail (d).
Now, we can calculate the heat energy gained by multiplying the force (F) by the distance (d).
Q = F * d
= 500 N * 0.18 m
= 90 J
Substituting the known values into the formula ΔT = (Q / (m * c)), we can calculate the change in temperature (ΔT):
ΔT = (90 J / (0.005 kg * 450 J/(kg * °C)))
= 40 °C
Therefore, the increase in temperature of the nail is approximately 40 °C.