A tennis ball of mass m = 0.068kg and speed v = 21m/s strikes a wall at a 45∘ angle and rebounds with the same speed at 45
What is the magnitude of the impulse given to the ball?
Impulse = 2*m*V*cos45
To find the magnitude of the impulse given to the ball, we can use the impulse-momentum theorem, which states that the impulse experienced by an object is equal to the change in momentum of that object.
The momentum of an object is given by the product of its mass and velocity. The change in momentum is the difference between the final momentum and the initial momentum.
Given:
Mass of the tennis ball, m = 0.068 kg
Initial velocity, v = 21 m/s
Angle of incidence, θ = 45°
First, we need to find the initial momentum (p1) and final momentum (p2) of the tennis ball.
Initial momentum (p1):
Since momentum is a vector quantity, we need to consider the horizontal and vertical components of the initial momentum separately.
Horizontal component:
The horizontal component of velocity remains the same throughout the collision because the wall is vertical. Therefore, the horizontal component of momentum remains constant.
p1_horizontal = m * v * cos(θ)
Vertical component:
The vertical component of velocity changes sign upon rebounding from the wall, but the magnitude remains the same.
p1_vertical = -m * v * sin(θ)
Now, let's calculate the initial momentum (p1) by adding the horizontal and vertical components:
p1 = √((p1_horizontal)^2 + (p1_vertical)^2)
Final momentum (p2):
Since the tennis ball rebounds with the same speed and angle, the magnitude of the final momentum (p2) will be the same as the initial momentum.
p2 = p1
Now, we can find the change in momentum (Δp) by subtracting the initial momentum from the final momentum:
Δp = p2 - p1
Finally, the magnitude of the impulse (J) is equal to the change in momentum:
J = |Δp|
By plugging in the given values and calculating, we can find the magnitude of the impulse given to the ball.
To find the magnitude of the impulse given to the ball, we need to calculate the change in momentum. Impulse is defined as the change in momentum of an object.
The momentum of an object is given by the equation:
momentum = mass × velocity
Before the ball strikes the wall, its momentum can be calculated as:
initial momentum = mass × initial velocity
m_1 = 0.068 kg × 21 m/s
After the ball rebounds, its momentum can be calculated as:
final momentum = mass × final velocity
m_2 = 0.068 kg × 21 m/s
The change in momentum, or impulse, is given by the equation:
impulse = final momentum - initial momentum
impulse = m_2 - m_1
impulse = (0.068 kg × 21 m/s) - (0.068 kg × 21 m/s)
impulse = 0 kg·m/s
Therefore, the magnitude of the impulse given to the ball is 0 kg·m/s.