A golf ball strikes a hard, smooth floor at an angle of 20.7 ° and, as the drawing shows, rebounds at the same angle. The mass of the ball is 0.0528 kg, and its speed is 40.2 m/s just before and after striking the floor. What is the magnitude of the impulse applied to the golf ball by the floor? (Hint: Note that only the vertical component of the ball's momentum changes during impact with the floor, and ignore the weight of the ball.)
2mvcosθ
2(0.0528 kg)(40.2 m/s)cos20.7=3.97 kg*m/s
To find the magnitude of the impulse applied to the golf ball by the floor, we need to use the principle of conservation of momentum. The impulse is equal to the change in momentum of the ball.
Step 1: Find the initial momentum of the ball just before striking the floor.
The initial momentum (p_i) is calculated by multiplying the mass of the ball (m) by its initial velocity (v_i).
p_i = m * v_i
Given:
Mass of the ball (m) = 0.0528 kg
Initial velocity (v_i) = 40.2 m/s
Substituting the given values:
p_i = 0.0528 kg * 40.2 m/s
Step 2: Find the final momentum of the ball just after striking the floor.
Since the ball rebounds at the same angle, the magnitude of its final velocity (v_f) will also be 40.2 m/s. However, the direction of the velocity vector will be opposite to the initial direction. Hence, we need to consider the negative sign.
The final momentum (p_f) is calculated as:
p_f = m * (-v_f)
Given:
Mass of the ball (m) = 0.0528 kg
Final velocity (v_f) = -40.2 m/s
Substituting the given values:
p_f = 0.0528 kg * (-40.2 m/s)
Step 3: Calculate the change in momentum during impact.
The change in momentum (Δp) is the difference between the final momentum and the initial momentum.
Δp = p_f - p_i
Substituting the values calculated in the previous steps:
Δp = [0.0528 kg * (-40.2 m/s)] - [0.0528 kg * 40.2 m/s]
Step 4: Calculate the magnitude of the impulse.
Since impulse (J) is equal to the change in momentum (Δp), we can write:
J = |Δp|
Taking the absolute value of the change in momentum, we get:
J = |[0.0528 kg * (-40.2 m/s)] - [0.0528 kg * 40.2 m/s]|
Substituting the values into the equation and calculating:
J = |(-2.12256 kg·m/s) - (2.12256 kg·m/s)|
J = 0
Hence, the magnitude of the impulse applied to the golf ball by the floor is zero.