A 0.145 kg baseball is moving at a speed of 15.0 meter/sec east toward the bat. The bat has 3.00x10^-3 seconds contact with the ball. As a result the ball flies back at 25.0 meter/sec west. What was the force (vector!) the bat exerted on the ball?
Well, isn't that quite the hit! It sounds like this baseball had a one-way ticket to reverseville. Now, let's calculate the force the bat exerted on the ball.
To do that, we can use Newton's second law, which states that force (F) is equal to mass (m) multiplied by the change in velocity (Δv), divided by the time interval (Δt). In equation form, it looks like this: F = m * Δv / Δt.
In this case, the mass (m) of the baseball is 0.145 kg, the change in velocity (Δv) is (25.0 m/s - (-15.0 m/s)), which simplifies to 40.0 m/s, and the time interval (Δt) is 3.00x10^-3 seconds.
So, plugging in the values, we have F = 0.145 kg * 40.0 m/s / (3.00x10^-3 s).
Calculating that out, we get F ≈ 1.933 N. But since the ball is moving in the opposite direction, the force vector would be in the westward direction.
In summary, the force the bat exerted on the ball is approximately 1.933 N west. That's quite the power play by the bat! Keep swinging for the fences, my friend!
To find the force exerted by the bat on the ball, we can use the impulse-momentum theorem, which states that the change in momentum of an object is equal to the force multiplied by the time it acts. Mathematically, it can be written as:
Impulse = Force × Time
We can find the change in momentum of the ball using the initial and final velocities:
Change in momentum = Final momentum - Initial momentum
To calculate the initial momentum of the ball, we can multiply its mass by its initial velocity. Similarly, the final momentum can be calculated by multiplying the mass by the final velocity.
The formula for momentum is given by:
Momentum = Mass × Velocity
Let's calculate the initial momentum first:
Initial momentum = mass × initial velocity
= 0.145 kg × 15.0 m/s
= 2.175 kg·m/s
Next, let's calculate the final momentum:
Final momentum = mass × final velocity
= 0.145 kg × (-25.0 m/s) (since the velocity is in the opposite direction)
= -3.625 kg·m/s
Now, calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
= -3.625 kg·m/s - 2.175 kg·m/s
= -5.8 kg·m/s
Finally, we can use the impulse-momentum theorem to find the force:
Force = Change in momentum / Time
= -5.8 kg·m/s / (3.00x10^-3 s)
= -1.9333 × 10^3 N
The force exerted by the bat on the ball is approximately -1.9333 × 10^3 N in the west direction. The negative sign indicates that the force is in the opposite direction of the initial velocity.
To find the force exerted by the bat on the ball, we can use the principle of conservation of momentum. According to this principle, the total momentum before the interaction is equal to the total momentum after the interaction.
1. First, let's find the initial momentum of the baseball:
Momentum = mass * velocity
Initial momentum = 0.145 kg * 15.0 m/s east
2. Next, let's find the final momentum of the baseball:
Final momentum = 0.145 kg * (-25.0 m/s west)
3. Since momentum is a vector quantity, we need to assign directions to the momenta. Let's consider east as positive and west as negative. So, the initial momentum is positive, and the final momentum is negative.
4. Now, we can set up the conservation of momentum equation:
Initial momentum = Final momentum
0.145 kg * 15.0 m/s = 0.145 kg * (-25.0 m/s)
We can cancel out the mass term and solve for the velocity:
15.0 m/s = -25.0 m/s
Due to the opposite directions, the magnitude of the final velocity is 25.0 m/s.
5. Finally, to find the force exerted by the bat, we can use Newton's second law of motion:
Force = (change in momentum) / time
Since we have the initial and final velocities, we can calculate the change in velocity:
Change in velocity = Final velocity - Initial velocity
Change in velocity = -25.0 m/s - 15.0 m/s
Change in velocity = -40.0 m/s
Now, we can substitute the values into the force equation:
Force = (0.145 kg * (-40.0 m/s)) / (3.00x10^-3 s)
Evaluating the above expression, we get the force exerted by the bat on the ball.