A ball of mass 1000g drops from a height of 5m and rebounded to a height of 2.5m. Calculate
I. It's kinetic energy before impact
ii. It's initial rebound ,velocity and kinetic energy
1. KE before impact=mgh=1kg*9.8N/kg*5m
2. initial rebound energy= mgh=1kg*9.8N/kg*2.5m
velocity? find from 1/2 m v^2=initial rebound energy solve for v
To calculate the kinetic energy before impact, we need to use the equation:
Kinetic Energy (KE) = (1/2) * mass * velocity^2
I. Calculate the kinetic energy before impact:
Given:
Mass of the ball (m) = 1000 grams = 1 kg
Height of the drop (h) = 5 m (which is the potential energy before the drop)
To find the velocity before impact, we can use the concept of conservation of energy.
Potential Energy (PE) before drop = Kinetic Energy (KE) before impact
PE = m * g * h
KE = (1/2) * m * v^2
Setting these two equations equal:
m * g * h = (1/2) * m * v^2
Now, we can cancel out the mass (m) on both sides:
g * h = (1/2) * v^2
Rearrange the equation and solve for v^2:
v^2 = 2 * g * h
Substituting the given values:
v^2 = 2 * 9.8 m/s^2 * 5 m
v^2 = 98 m^2/s^2
Taking the square root of both sides:
v = √(98) m/s
v ≈ 9.90 m/s
Now, calculate the kinetic energy before impact using the calculated velocity:
KE = (1/2) * m * v^2
KE = (1/2) * 1 kg * (9.90 m/s)^2
KE ≈ 48.51 Joules
Therefore, the kinetic energy before impact is approximately 48.51 Joules.
II. Calculate the initial rebound velocity and kinetic energy:
Given:
Height of the rebound (h') = 2.5 m
We can again use the concept of conservation of energy to find the velocity at the rebound:
Potential Energy (PE) at rebound = Kinetic Energy (KE) at rebound
PE = m * g * h'
KE = (1/2) * m * v'^2
Setting these two equations equal:
m * g * h' = (1/2) * m * v'^2
Cancel out the mass (m) on both sides:
g * h' = (1/2) * v'^2
Rearrange the equation and solve for v'^2:
v'^2 = 2 * g * h'
Substituting the given values:
v'^2 = 2 * 9.8 m/s^2 * 2.5 m
v'^2 = 49 m^2/s^2
Taking the square root of both sides:
v' = √(49) m/s
v' = 7 m/s
Now, calculate the kinetic energy at rebound using the calculated velocity:
KE = (1/2) * m * v'^2
KE = (1/2) * 1 kg * (7 m/s)^2
KE = 24.5 Joules
Therefore, the initial rebound velocity is 7 m/s and the kinetic energy at rebound is 24.5 Joules.