A baseball of mass 0.13 kg, moving horizontally with a momentum of 4 kg¡Pm/s, is struck head-on by a baseball bat with an impulse of 10 N¡Ps. What is the speed of the baseball after it is struck?
_______m/s
To find the speed of the baseball after it is struck, we need to use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, provided there are no external forces acting on the system.
In this case, the momentum before the event (collision) is given as 4 kg·m/s, and the impulse during the collision is given as 10 N·s.
Impulse can be defined as the change in momentum:
Impulse = Change in momentum
In equation form:
Impulse = (Final momentum) - (Initial momentum)
Therefore, we can rearrange the equation to solve for the final momentum:
(Final momentum) = Impulse + (Initial momentum)
Substituting the given values:
(Final momentum) = 10 N·s + 4 kg·m/s
(Final momentum) = 14 kg·m/s
Since momentum is defined as the product of mass and velocity:
(Final momentum) = (mass) · (final velocity)
We can rearrange this equation to solve for the final velocity:
(final velocity) = (Final momentum) / (mass)
Substituting the values:
(final velocity) = 14 kg·m/s / 0.13 kg
(final velocity) ≈ 107.69 m/s
Therefore, the speed of the baseball after it is struck is approximately 107.69 m/s.
To find the speed of the baseball after it is struck, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
Here's how we can solve the problem step by step:
1. Start by calculating the initial momentum of the baseball (p_initial). Given that the baseball has a mass (m) of 0.13 kg and a momentum (p_initial) of 4 kg•m/s, we can use the formula:
p_initial = m * v_initial
Rearranging the formula, we find:
v_initial = p_initial / m
Plugging in the given values, we get:
v_initial = 4 kg•m/s / 0.13 kg
2. Next, we need to calculate the change in momentum of the baseball, also known as impulse (J). We are given that the bat exerts an impulse of 10 N•s.
Impulse (J) = 10 N•s
3. Now, we need to find the final momentum of the baseball (p_final) after it is struck. Since we know the change in momentum (impulse) and the initial momentum (p_initial), we can use the equation:
J = p_final - p_initial
Rearranging the equation, we get:
p_final = J + p_initial
Plugging in the known values, we get:
p_final = 10 N•s + (0.13 kg * v_initial)
4. Finally, to find the speed (v_final) of the baseball after it is struck, we divide the final momentum (p_final) by the mass (m) of the baseball:
v_final = p_final / m
Plugging in the values we found, we get:
v_final = (10 N•s + (0.13 kg * v_initial)) / 0.13 kg
By following these steps and performing the necessary calculations, you can find the value of v_final, which will give you the speed of the baseball after it is struck.