A 2.4kg ball falling vertically hits the floor with a speed of 2.5m/s and rebounds with a speed of 1.5m/s. What is the impulse exerted on the floor?
To find the impulse exerted on the floor, we can use the impulse-momentum principle, which states that the change in momentum of an object is equal to the impulse applied to it.
Impulse (J) is defined as the product of the force (F) applied to an object and the time interval (Δt) over which the force is applied. Mathematically, it can be expressed as:
J = F × Δt
The impulse can also be calculated as the change in momentum (Δp) of the object:
J = Δp
In this case, the impulse exerted on the floor can be determined by calculating the change in momentum of the ball.
The momentum (p) of an object is defined as the product of its mass (m) and its velocity (v):
p = m × v
The change in momentum (Δp) is equal to the final momentum minus the initial momentum:
Δp = pfinal - pinitial
The initial momentum of the ball can be calculated by multiplying its mass (m) and initial velocity (v):
pinitial = m × vinitial
The final momentum of the ball can be calculated by multiplying its mass (m) and final velocity (v):
pfinal = m × vfinal
Substituting these formulas back into the equation for change in momentum:
Δp = pfinal - pinitial = (m × vfinal) - (m × vinitial)
Now let's substitute the given values:
m (mass) = 2.4 kg
vinitial (initial velocity) = 2.5 m/s
vfinal (final velocity) = -1.5 m/s (since the ball rebounds in the opposite direction)
Δp = (2.4 kg × -1.5 m/s) - (2.4 kg × 2.5 m/s)
Simplifying the equation:
Δp = (-3.6 kg·m/s) - (6 kg·m/s)
Δp = -9.6 kg·m/s
The impulse exerted on the floor is -9.6 kg·m/s. The negative sign indicates that the impulse is in the opposite direction of the initial momentum of the ball.
To find the impulse exerted on the floor, we first need to calculate the change in momentum of the ball.
The momentum of an object is given by the equation:
Momentum = Mass * Velocity
The initial momentum of the ball before it hits the floor can be calculated using the mass and initial velocity:
Initial Momentum = Mass * Initial Velocity
Substituting the given values:
Initial Momentum = 2.4 kg * 2.5 m/s
Next, let's calculate the final momentum of the ball after it rebounds from the floor:
Final Momentum = Mass * Final Velocity
Substituting the given values:
Final Momentum = 2.4 kg * 1.5 m/s
The change in momentum of the ball during the collision can be calculated by subtracting the final momentum from the initial momentum:
Change in Momentum = Final Momentum - Initial Momentum
Substituting the calculated values:
Change in Momentum = (2.4 kg * 1.5 m/s) - (2.4 kg * 2.5 m/s)
Now, evaluating the expression:
Change in Momentum = (3.6 kg m/s) - (6.0 kg m/s)
Change in Momentum = -2.4 kg m/s
The negative sign indicates that the direction of the momentum has reversed during the collision. Since impulse is defined as the change in momentum, the impulse exerted on the floor can be calculated as the absolute value of the change in momentum:
Impulse = |-2.4 kg m/s|
Therefore, the impulse exerted on the floor is 2.4 kg m/s.
Impulse = m*V1-m*V2
Impulse = 2.4*2.5 - 2.4*1.5 = 2.4kgm/s