A 2.00 kg box slides down a rough incline plane from a height h of 1.99 m. The box had a speed of 2.77 m/s at the top and a speed of 2.34 m/s at the bottom. Calculate the mechanical energy lost due to friction (as heat, etc.)
If I were to calculate the energy lost, it would be from the potential energy, correct?
Yes, you are correct. To calculate the mechanical energy lost due to friction, you would start by calculating the initial potential energy and final potential energy of the box. The difference between these two values will give you the mechanical energy lost.
To calculate the mechanical energy lost due to friction, we need to find the initial potential energy and the final kinetic energy of the box.
The mechanical energy of the system (box) is the sum of its potential energy (PE) and kinetic energy (KE).
1. Find the initial potential energy (PEi):
The potential energy is given by the equation PEi = m * g * h, where m is the mass of the box, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height of the incline plane.
In this case, the mass (m) is 2.00 kg, and the height (h) is 1.99 m. So we can calculate PEi = 2.00 kg * 9.8 m/s² * 1.99 m.
2. Find the final kinetic energy (KEf):
The kinetic energy is given by the equation KEf = 0.5 * m * v², where m is the mass of the box, and v is the velocity of the box.
In this case, the mass (m) is still 2.00 kg, and the velocity (v) at the bottom is 2.34 m/s. So we can calculate KEf = 0.5 * 2.00 kg * (2.34 m/s)².
3. Calculate the mechanical energy lost due to friction:
The mechanical energy lost is the difference between the initial potential energy and the final kinetic energy lost to friction.
It can be calculated by subtracting the final kinetic energy (KEf) from the initial potential energy (PEi) lost = PEi - KEf.
Substituting the values into the equations, you can calculate the mechanical energy lost due to friction.
energy at top = m g h + (1/2) m v^2
= 2 * 9.81 * 1.99 + .5*2 (2.77)^2
energy at bottom = (1/2) m v^2
= .5*2(2.34)^2
difference is loss to friction. If there were no loss to friction of course it would be going FASTER at the bottom :)