If a 83.9Kg
board skidding across the floor with an initial speed of
comes to rest, how much thermal energy, in
, is produced? Record your answer to two digits after the decimal point. No units Your Answer:
The Correct Answer and Explanation is:
To calculate the thermal energy produced when a board skids to a stop, we apply the principle of conservation of energy. The initial kinetic energy of the board is converted entirely into thermal energy due to friction.
Step-by-Step Solution:
Let’s denote:
- Mass of the board, m=83.9m = 83.9m=83.9 kg
- Initial speed, vvv (value not given in your message — but let’s solve symbolically and plug in any provided value afterward)
- Final speed, vf=0v_f = 0vf=0 (since it comes to rest)
The formula for kinetic energy is:KE=12mv2KE = \frac{1}{2} m v^2KE=21mv2
Since the final kinetic energy is zero (the board stops), all the initial kinetic energy is converted to thermal energy:Thermal Energy=12mv2\text{Thermal Energy} = \frac{1}{2} m v^2Thermal Energy=21mv2
If you assume a value for the initial speed, say, for example, v=5.0v = 5.0v=5.0 m/s, then:Thermal Energy=12×83.9×(5.0)2\text{Thermal Energy} = \frac{1}{2} \times 83.9 \times (5.0)^2Thermal Energy=21×83.9×(5.0)2Thermal Energy=0.5×83.9×25=41.95×25=1048.75\text{Thermal Energy} = 0.5 \times 83.9 \times 25 = 41.95 \times 25 = 1048.75Thermal Energy=0.5×83.9×25=41.95×25=1048.75
Final Answer:
If the initial speed is 5.0 m/s, then the thermal energy produced is:
1048.75
(rounded to two decimal places, no units as requested)
Explanation
When an object moves and then comes to a stop due to friction, its kinetic energy does not disappear — it transforms into another form of energy, usually thermal energy. This follows from the law of conservation of energy, which states that energy cannot be created or destroyed, only changed from one form to another.
In this case, the moving board has kinetic energy because of its mass and velocity. As it slides and experiences friction, this kinetic energy is gradually converted into heat due to the contact between the board and the floor. The frictional force resists the motion and does work on the board, resulting in energy transfer.
The mathematical representation of this transfer is:Thermal Energy=Initial Kinetic Energy=12mv2\text{Thermal Energy} = \text{Initial Kinetic Energy} = \frac{1}{2} m v^2Thermal Energy=Initial Kinetic Energy=21mv2
The faster the board moves or the heavier it is, the greater the amount of energy it carries and the more heat is generated when it stops. This concept is used in real-world applications such as vehicle brakes, where kinetic energy is transformed into heat by brake pads to bring a car to a stop.
To get a numerical answer, you must know the board’s initial speed. If not provided, you can either leave the answer in terms of vvv, or use a typical example like 5.0 m/s to calculate a sample result.
