A 16.0 - kg descends a slide 2.50 m high and reaches the bottom with a speed of 2.25 m/s. How much thermal energy due to firciton was generated in the process?
for this I keep on getting 432.5 J but the back of the book tells me that the answer is 352 J and I do not see how to get this answer
I did the PE at the the top of the slide minus the KE at the bottom and got 432.5 J apparently I'm doing soemthing wrong thanks
friction=mgh-1/2 m v^2
= m(gh-.5 v^2)=16(9.8*2.5-.5*2.25^2)
=352 Joules
To calculate the thermal energy generated due to friction, we need to first find the initial potential energy (PE) at the top of the slide and the final kinetic energy (KE) at the bottom of the slide.
The initial potential energy can be calculated using the formula:
PE = m * g * h
where m is the mass (16.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the slide (2.50 m).
PE = 16.0 kg * 9.8 m/s^2 * 2.50 m
PE = 392 J
Next, we need to find the final kinetic energy using the formula:
KE = (1/2) * m * v^2
where m is the mass (16.0 kg) and v is the final velocity (2.25 m/s).
KE = (1/2) * 16.0 kg * (2.25 m/s)^2
KE = 40.5 J
Finally, we can calculate the thermal energy generated due to friction by subtracting the final kinetic energy from the initial potential energy:
Thermal Energy = PE - KE
Thermal Energy = 392 J - 40.5 J
Thermal Energy = 351.5 J (rounded to one decimal place)
Therefore, the correct answer is approximately 352 J, which is consistent with the answer provided in the book. It seems like there might have been a small calculation error in your previous attempt.