Calculating Temperature Change of a Lead Ball Dropped from 106.0 m

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In summary, a lead ball with an initial temperature of 25 °C is dropped from a height of 106.0 m and does not bounce upon impact. Assuming all the energy from the fall is converted into heat, the temperature of the ball can be found using the equation Q=cm(deltaT), where Q represents the energy, c is the specific heat of lead (128 J/kg°C), and deltaT is the change in temperature. The mass of the ball is not needed in this calculation. Additionally, the kinetic energy of the ball is directly proportional to its mass.
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hatingphysics
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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!
 
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  • #2
Maybe the mass cancels out... What can you say about the kinetic energy of the ball as a function of the mass...
 
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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.
 

FAQ: Calculating Temperature Change of a Lead Ball Dropped from 106.0 m

What is energy to heat conversion?

Energy to heat conversion is the process of converting one form of energy, such as electrical energy or chemical energy, into heat energy. This is achieved through various mechanisms, such as combustion, friction, or electrical resistance.

How is energy converted to heat?

Energy can be converted to heat through several different processes, including combustion, friction, and electrical resistance. In combustion, energy from a fuel source is converted to heat through a chemical reaction. Friction converts mechanical energy into heat energy through the resistance of two surfaces rubbing against each other. Electrical resistance converts electrical energy into heat energy through the resistance of a material to the flow of electricity.

What are some examples of energy to heat conversion?

Some common examples of energy to heat conversion include burning wood for heat, turning on an electric stove, and rubbing your hands together to warm them up. Other examples include the use of a furnace, a hairdryer, or a car engine.

What is the law of conservation of energy and how does it relate to energy to heat conversion?

The law of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another. This means that energy to heat conversion follows this law, as the energy being converted from one form to heat energy already existed in another form.

How is energy to heat conversion used in everyday life?

Energy to heat conversion is used in a variety of ways in everyday life. For example, it is used to heat homes and buildings, cook food, and power various appliances and electronic devices. It is also used in industrial processes, such as in the production of steel or the generation of electricity. Additionally, our bodies also convert energy to heat in order to maintain a constant body temperature.

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