# Force applied: calculating increase in temperature (work mostly done, )

• spidey64
In summary, the conversation discusses the process of calculating the increase in temperature of a nail when hit by a hammer with a force of 500N. The length of the nail is .06m and the work done is 30 Joules. The specific heat capacity of the nail is 450 J/kg *C. The formula Q/(change in Temp x mass) is used to find the specific heat capacity, and the value of (change in Temp x m) is determined to be .0667 kg*C. However, there is uncertainty about how to find the mass of the nail in order to isolate the temperature value.
spidey64
Ok, I need to calculate the increase in temperature of a nail hit by a hammer with force of 500N. The length of the nail is .06m, so the work done and, I'm assuming, the energy added to the nail (Q) is 30 Joules. The specific heat capacity of the nail is 450 J/kg *C(degrees Celsius). By using the formula for finding the specific heat capacity : Q/(change in Temp x mass), I then found that the (change in Temp x m) = .0667 kg*C, but how the heck do I find the mass of the nail to single out the temp value?

really? no ideas at all? or am I going down the wrong path, or anything?

Hello,

Thank you for sharing your calculations with me. I would suggest using the formula for work, W = Fd, where F is the force applied and d is the distance the force is applied over. In this case, the force is 500N and the distance is 0.06m, so the work done is 30 Joules, as you have correctly calculated.

To find the change in temperature, we can use the formula Q = mcΔT, where Q is the energy added to the nail, m is the mass of the nail, c is the specific heat capacity, and ΔT is the change in temperature. We already know Q and c, so we just need to find the mass of the nail.

To find the mass of the nail, we can use the formula m = W/g, where W is the work done and g is the acceleration due to gravity (9.8 m/s^2). Plugging in our values, we get m = 30J/9.8 m/s^2 = 3.06 kg.

Now, we can plug in all our values into the formula Q = mcΔT to find the change in temperature. We get 30J = (3.06 kg)(450 J/kg *C)(ΔT), which gives us a change in temperature of 0.022 degrees Celsius.

I hope this helps. Let me know if you have any further questions.

Best,

## 1. How do you calculate the increase in temperature from a force applied?

The increase in temperature from a force applied can be calculated using the formula Q = F * d * α, where Q is the change in temperature, F is the force applied, d is the distance over which the force is applied, and α is the coefficient of thermal expansion for the material.

## 2. What is the relationship between work done and increase in temperature?

The work done on an object is directly proportional to the increase in temperature. This means that the greater the work done, the greater the increase in temperature will be.

## 3. Can the increase in temperature be negative when a force is applied?

No, the increase in temperature will always be positive when a force is applied. This is because work done is a measure of energy transferred, and energy cannot have a negative value.

## 4. How does the material of an object affect the increase in temperature from a force applied?

The material of an object can affect the increase in temperature due to its specific heat capacity and coefficient of thermal expansion. Different materials have different abilities to absorb and retain heat, and their expansion rates also vary. This means that the increase in temperature may vary for different materials when the same force is applied.

## 5. Is the increase in temperature from a force applied always the same for all objects?

No, the increase in temperature can vary for different objects depending on their material, size, and shape. As mentioned before, different materials have different thermal properties, and the amount of work done may also vary depending on the size and shape of the object.

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