A 2 kg ball is rolled down a hill 25 m tall. When it reaches the bottom of the hill it is traveling at 15.1 m/s. How much energy was dissipated due to friction?
To calculate the energy dissipated due to friction, you need to determine the initial potential energy at the top of the hill and the final kinetic energy at the bottom. The difference between these two values will tell you the amount of energy dissipated.
First, let's calculate the initial potential energy (PE) of the ball at the top of the hill. The potential energy of an object at a certain height is given by the formula:
PE = m * g * h
where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height.
PE = 2 kg * 9.8 m/s² * 25 m
PE = 490 J
Next, we need to calculate the final kinetic energy (KE) of the ball at the bottom of the hill. The kinetic energy of an object is given by the formula:
KE = 1/2 * m * v²
where m is the mass of the object and v is its velocity.
KE = 1/2 * 2 kg * (15.1 m/s)²
KE = 453.31 J
Now, calculate the energy dissipated due to friction:
Energy dissipated = PE - KE
Energy dissipated = 490 J - 453.31 J
Energy dissipated = 36.69 J
Therefore, approximately 36.69 Joules of energy were dissipated due to friction.