Rubbing your hands together warms them by converting work into thermal energy. If a woman rubs her hands back and forth for a total of 14 rubs a distance of 7.50 cm each and with a frictional force averaging 30.0 N, what is the temperature increase? The mass of tissue warmed is only 0.100 kg, mostly in the palms and fingers.

To calculate the temperature increase, we need to find the amount of work done by the frictional force applied during the rubbing process. The formula for work is given by:

Work = Force x Distance

Since the force is constant and the distance is the same for each rub, we can calculate the total work done by multiplying the average force by the total distance covered:

Total Work = Average Force x Total Distance

The total distance covered is given by the number of rubs (14) multiplied by the distance of each rub (7.50 cm). We need to convert this distance to meters to maintain consistent units:

Total Distance = 14 x 7.50 cm = 0.14 m

Now we can substitute the known values into the equation to calculate the total work:

Total Work = 30.0 N x 0.14 m = 4.2 Joules

Next, we will use the formula for thermal energy:

Thermal Energy = mass x specific heat capacity x temperature increase

Note that the specific heat capacity of tissue is not given, so we will assume a value of 3,200 J/(kg⋅°C) based on the specific heat capacity of water.

Solving for the temperature increase gives us:

Temperature Increase = Thermal Energy / (mass x specific heat capacity)

Temperature Increase = 4.2 J / (0.100 kg x 3,200 J/(kg⋅°C))

Temperature Increase ≈ 0.013°C

Therefore, the temperature increase resulting from the rubbing of the hands is approximately 0.013°C.

To calculate the temperature increase, we need to consider the work done by the frictional force and the thermal energy generated.

First, let's calculate the work done:
Work (W) = Force (F) × Distance (d)
W = 30.0 N × 14 rubs × 0.075 m (since 7.50 cm equals 0.075 m)
W = 31.5 J (joules)

Next, we need to calculate the thermal energy generated. We can assume that all the work done is converted into thermal energy:
Thermal energy (Q) = Work (W)
Q = 31.5 J

Now, let's calculate the temperature increase using the specific heat formula:
Q = m × c × ΔT
Where:
Q is the thermal energy (in Joules),
m is the mass of tissue warmed (in kilograms),
c is the specific heat capacity of the tissue (in J/kg°C),
ΔT is the change in temperature (in °C).

We are given:
Q = 31.5 J
m = 0.100 kg

However, we need to determine the specific heat capacity of the tissue. The specific heat capacity represents the amount of energy required to raise the temperature of a substance by 1 degree Celsius. Since specific heat capacity varies depending on the substance, we need this information to continue.

If the specific heat capacity of the tissue is known, you can use the equation to solve for ΔT, the change in temperature. However, without the specific heat capacity value, we cannot determine the exact temperature increase.