A 2.7 kg ball strikes a wall with a velocity of 7.8 m/s to the left. The ball bounces off with a velocity of 6.6 m/s to the right. If the ball is in contact with the wall for 0.19 s, what is the constant force exerted on the ball by the wall?
F=(delta P)/T
(mv-mv)/T
To find the constant force exerted on the ball by the wall, we can use the impulse-momentum principle. The impulse-momentum principle states that the change in momentum of an object is equal to the impulse applied to it. In equation form, this principle is expressed as:
Impulse = Change in Momentum
Impulse can be calculated by multiplying the force applied to an object by the time for which the force is applied. In this case, the force we want to find is constant, so we have:
Impulse = Force × Time
The change in momentum can be calculated by subtracting the initial momentum from the final momentum. In this case, momentum is equal to the mass of the ball multiplied by its velocity. So we have:
Change in Momentum = Final Momentum - Initial Momentum
Let's calculate the initial momentum of the ball. The initial momentum is determined by the mass of the ball and its initial velocity. The mass of the ball is given as 2.7 kg, and its initial velocity is 7.8 m/s to the left. Since momentum is a vector quantity, we need to take the direction into account and assign a negative sign to the momentum. Thus, the initial momentum is:
Initial Momentum = - (mass × initial velocity)
= - (2.7 kg × 7.8 m/s)
Next, let's calculate the final momentum of the ball. The final momentum is determined by the mass of the ball and its final velocity. The mass of the ball is still 2.7 kg, and its final velocity is 6.6 m/s to the right. Again, taking the direction into account, the final momentum is:
Final Momentum = (mass × final velocity)
= 2.7 kg × 6.6 m/s
Now we can calculate the change in momentum by subtracting the initial momentum from the final momentum:
Change in Momentum = Final Momentum - Initial Momentum
Finally, substitute the values into the equation for impulse:
Impulse = Force × Time
Solve for force to find the constant force exerted on the ball by the wall.