A 0.2-kg billiard ball that is moving at 9.8 m/s strikes the bumper of a pool table and bounces straight back at 2.9 m/s. The collision lasts 0.05s. Calculate the average force exerted on the ball by the bumper.
find the change in momentum
0.2 ( 9.8 - - 2.9) = 0.2* 12.7 = 2.54 kg m/s
force = change in momentum / time = 2.54 / 0.05 Newtons
Why did the billiard ball go to the pool party? Because it knew the bouncer would give it a good "force" to bounce back! But let's get serious for a moment and calculate the average force.
We can use the impulse-momentum principle to find the force exerted on the ball. The impulse is given by the change in momentum:
Impulse = ∆p = m ∆v,
where m is the mass of the ball and ∆v is the change in velocity. In this case, the initial velocity (v1) is 9.8 m/s, the final velocity (v2) is -2.9 m/s (since it bounces back), and the duration of the collision (Δt) is 0.05 seconds.
So, the change in momentum is:
∆p = m(v2 - v1).
Plugging in the values, we get:
∆p = 0.2 kg (-2.9 m/s - 9.8 m/s).
Calculating this gives us ∆p = -2.34 kg·m/s.
Now, we know that impulse is also equal to the average force multiplied by the time of collision:
Impulse = Favg Δt.
Rearranging the equation, we find:
Favg = ∆p / Δt.
Plugging in the values, we get:
Favg = -2.34 kg·m/s / 0.05 s.
Calculating this gives us Favg = -46.8 N.
Therefore, the average force exerted on the ball by the bumper is approximately 46.8 Newtons.
To calculate the average force exerted on the ball by the bumper, we can use Newton's second law of motion, which states that the force is equal to the change in momentum divided by the time taken.
The initial momentum of the ball before the collision can be calculated using the equation:
Initial momentum = mass × initial velocity
Let's calculate it:
Initial momentum = 0.2 kg × 9.8 m/s = 1.96 kg·m/s
Similarly, the final momentum of the ball after the collision can be calculated:
Final momentum = mass × final velocity
Final momentum = 0.2 kg × (-2.9 m/s) = -0.58 kg·m/s
The change in momentum can be calculated by subtracting the final momentum from the initial momentum:
Change in momentum = Final momentum - Initial momentum
Change in momentum = -0.58 kg·m/s - 1.96 kg·m/s = -2.54 kg·m/s
Next, we can calculate the average force exerted on the ball using the equation:
Average force = Change in momentum / Time taken
Average force = -2.54 kg·m/s / 0.05 s = -50.8 N
It's important to note that the negative sign indicates that the force is acting in the opposite direction to the motion of the ball.
To calculate the average force exerted on the ball by the bumper, we can use Newton's second law of motion, which states that the force exerted on an object is equal to the rate of change of its momentum. Mathematically, it can be expressed as:
Force = (final momentum - initial momentum) / time
First, let's calculate the initial momentum of the billiard ball. Momentum is the product of an object's mass and its velocity:
Initial momentum = mass * initial velocity
Plugging in the given values:
Mass = 0.2 kg
Initial velocity = 9.8 m/s
Initial momentum = 0.2 kg * 9.8 m/s
Next, let's calculate the final momentum of the billiard ball. Since the ball bounces straight back, its direction changes, but its magnitude remains the same:
Final momentum = mass * final velocity
Plugging in the given values:
Mass = 0.2 kg
Final velocity = -2.9 m/s (negative, to indicate the opposite direction)
Final momentum = 0.2 kg * (-2.9 m/s)
Now that we have the initial and final momentum, we can find the average force exerted on the ball by the bumper:
Average force = (final momentum - initial momentum) / time
Plugging in the given value for time:
Time = 0.05 s
Average force = (0.2 kg * (-2.9 m/s) - 0.2 kg * 9.8 m/s) / 0.05 s
Simplifying the equation:
Average force = (0.2 kg * (-2.9 m/s) + (-0.2 kg * 9.8 m/s)) / 0.05 s
Calculating the numerator:
Average force = (-0.58 Ns + (-1.96 Ns)) / 0.05 s
Average force = -2.54 Ns / 0.05 s
Average force = -50.8 N
Therefore, the average force exerted on the billiard ball by the bumper is 50.8 Newtons.