a bouncing ball of mass 200g leaves the ground with a kinetic energy of 10J
a)if the ball rises vertically, calculate the maximum height it is likely to reach.
b)in practice, the ball rarely reaches the maximum height. explain why this is so.
Use kinetic energy
Make sure that if you have Joules, you have kg, not grams.
K = 1/2 mv^2
10 = 1/2 (.2) v^2
10 = .1v^2
100=v^2
10 = v
So, the motion of the ball is
h = 10t - 4.9t^2
max height at t = -10/-9.8 = 1.02
h(1.02) = 5.10
The ball should come pretty close to this height, since we know its initial velocity. The only thing that could affect its height is air resistance. Any inelasticity of the rubber does not come into play, since we are only analyzing its motion after it has already left the ground.
please help please i find this difficult if someone could just explain please
dr bob can you help
help if you can
I'm sorry, but I'm a real dummy in physical science.
do you no anyone who know how to do this, this is due in school
a) To calculate the maximum height the ball will reach, we can apply the principle of conservation of energy.
Initially, the ball has a kinetic energy of 10J. As it rises vertically, it loses this kinetic energy and gains potential energy due to the gravitational pull. At the highest point, all of the kinetic energy is converted into potential energy.
The potential energy (PE) is given by the formula PE = mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height.
Given:
Mass of the ball (m) = 200g = 0.2kg
Kinetic energy (KE) = 10J
We can equate the initial kinetic energy with the potential energy at the highest point:
KE = PE
10J = mgh
Substituting the values, we have:
10J = 0.2kg * 9.8 m/s^2 * h
Simplifying the equation, we find:
h = 10J / (0.2kg * 9.8 m/s^2)
h = 5m
Therefore, the maximum height the ball is likely to reach is 5 meters.
b) In practice, the ball rarely reaches the maximum height due to various factors that cause energy losses. Some of these factors include air resistance, friction between the ball and the surface, and imperfections in the ball's bounce.
Air resistance: When the ball is in motion, it experiences air resistance, which opposes its upward movement. This resistance causes a loss of kinetic energy, reducing the height the ball can reach compared to the maximum theoretical value.
Friction: Friction between the ball and the surface it bounces from also causes energy losses. As the ball collides with the ground, some of its kinetic energy is transformed into heat energy due to the friction between the ball and the surface.
Imperfections in the ball's bounce: The ball may not perfectly conserve energy during the bounce. Some energy may be absorbed or dissipated within the ball due to its internal structure or material properties. This loss of energy reduces the height the ball can achieve in subsequent bounces.
Overall, these factors result in the ball rarely reaching the maximum height predicted by the conservation of energy principle.