A 0.10 kilogram ball dropped vertically from a height of 1.0 meter above the floor bounces back to a height of 0.80 meter. The mechanical energy lost by the ball as it bounces is aprox.
a. 0.080 J
b. 0.20 J
c. 0.30 J
d. 0.78 J
B.) (.10kg)(10 m/s^2)(0.20m) = .20J
.20
To determine the mechanical energy lost by the ball as it bounces, we can use the principle of conservation of mechanical energy. According to this principle, the total mechanical energy of an object remains constant as long as only conservative forces, such as gravity, are acting on it.
The mechanical energy of an object can be divided into two components: kinetic energy (KE) and potential energy (PE). Kinetic energy is the energy of motion, while potential energy is the energy associated with an object's position or height above a reference point.
When the ball is dropped from a height of 1.0 meter, it has potential energy equal to its gravitational potential energy. This can be calculated using the formula PE = mgh, where m is the mass of the ball (0.10 kg), g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height (1.0 m).
PE = (0.10 kg) * (9.8 m/s²) * (1.0 m)
PE = 0.98 J
At the highest point of the bounce, the ball has potential energy equal to the potential energy it had before being dropped. Therefore, at a height of 0.80 meters, the potential energy is given by PE = mgh:
PE = (0.10 kg) * (9.8 m/s²) * (0.80 m)
PE = 0.784 J
The mechanical energy lost by the ball as it bounces can be calculated by subtracting the final potential energy from the initial potential energy:
Mechanical energy lost = Initial potential energy - Final potential energy
Mechanical energy lost = 0.98 J - 0.784 J
Mechanical energy lost ≈ 0.196 J
Based on the given answer choices, the closest value to 0.196 J is option b. Therefore, the mechanical energy lost by the ball as it bounces is approximately 0.20 J.
E=mgh1-mgh2=mg(h1-h2)=
=0.1•9.8(1-0.8)=0.78 J