Calculating Temperature Change of a Lead Ball Dropped from 106.0 m

[hatingphysics]

A lead ball, with an initial temperature of 25 °C, is released from a height of 106.0 m. It does not bounce when it hits a hard surface. Assume all the energy of the fall goes into heating the lead. Find the temperature in °C of the ball after it hits. (You do not need to enter the units.) Data: c of lead = 128 [(J)/(kg·° C)].

I don't know where to go in this problem

I know you use Q=cm(deltaT) But I don't know what the mass and Q are so where do I go with this equation? Please help me out!

 

[berkeman]

Maybe the mass cancels out... What can you say about the kinetic energy of the ball as a function of the mass...

 

[kyle8921]

I would approach this problem by first identifying the variables and information given. We know the specific heat capacity of lead (c=128 J/kg·°C), the initial temperature of the lead ball (25 °C), and the height it was dropped from (106.0 m). We also know that all the energy from the fall goes into heating the lead ball.

From this, we can use the equation Q=mc(deltaT) to solve for the change in temperature (deltaT) of the lead ball. The mass (m) of the lead ball can be calculated using its density and volume, or it can be provided in the problem. Once we have all the values, we can plug them into the equation and solve for deltaT.

After the lead ball hits the hard surface, it will have reached its maximum temperature. We can then add the change in temperature (deltaT) to the initial temperature (25 °C) to find the final temperature of the lead ball. It is important to note that the final temperature will be in Kelvin, so we will need to convert it to Celsius by subtracting 273.15.

In summary, to find the temperature of the lead ball after it hits the hard surface, we need to use the specific heat capacity of lead, the initial temperature, and the height it was dropped from to calculate the change in temperature. This change in temperature can then be added to the initial temperature to find the final temperature in °C.