a 500g ball traveling with a velocity of 5m/s strikes a vertical wall rebounds with a velocity of 4m/s
Find a) change in pressure of the ball
b) Joule of the collision
To find the change in pressure of the ball and the Joule of the collision, we need to apply Newton's second law of motion, as well as the equation for kinetic energy.
a) Change in pressure of the ball:
The change in pressure can be calculated using the formula:
ΔP = 2mΔv / A
Where:
- ΔP is the change in pressure
- m is the mass of the ball (500g)
- Δv is the change in velocity (final velocity - initial velocity)
- A is the surface area of the ball that collides with the wall (assuming it is a perfect sphere, the surface area can be calculated using the formula: A = 4πr², where r is the radius of the ball)
In this case, Δv = 4m/s - 5m/s = -1m/s (since the ball rebounds in the opposite direction)
Considering the mass of the ball is 500g, we can convert it to kg by dividing it by 1000: 500g / 1000 = 0.5kg.
Now, we need to find the surface area of the ball. Assuming the ball is a perfect sphere, we can calculate the radius of the ball from its mass. The formula to calculate the radius is:
m = (4/3)πr³
0.5kg = (4/3)πr³
Solving for r, we get:
r = ∛(0.5kg * 3 / (4π))
r ≈ 0.282m
Now, we can calculate the surface area of the ball:
A = 4πr²
A = 4π(0.282m)²
A ≈ 1.002m²
Substituting the values into the formula for ΔP:
ΔP = 2(0.5kg)(-1m/s) / 1.002m²
ΔP ≈ -0.996 Pa
Therefore, the change in pressure of the ball is approximately -0.996 Pa.
b) Joule of the collision:
The Joule of the collision represents the change in kinetic energy. Kinetic energy is given by the formula:
KE = (1/2)mv²
Where:
- KE is the kinetic energy
- m is the mass of the ball (500g)
- v is the velocity of the ball
For the initial velocity, v = 5m/s, and for the final (rebound) velocity, v = 4m/s.
Initial kinetic energy:
KE_initial = (1/2)(0.5kg)(5m/s)²
KE_initial = (1/2)(0.5)(25)
KE_initial = 6.25 Joules
Final kinetic energy:
KE_final = (1/2)(0.5kg)(4 m/s)²
KE_final = (1/2)(0.5)(16)
KE_final = 4 Joules
Joule of the collision (change in kinetic energy):
Joule = KE_final - KE_initial
Joule = 4 Joules - 6.25 Joules
Joule ≈ -2.25 Joules
Therefore, the Joule of the collision is approximately -2.25 Joules.