a pool player imports an impulse of 3.2 N*s to a stationary 0.25-kg cue ball with a cue stick what is the speed of the ball just after impact
The impulse equals the change in momentum, which is (mass) x(velocity change.
Solve for the velcoity change, which is the same as the final velocity in this case.
I got 12.8 m/s, which is 13 m/s after sig figs.
To find the speed of the ball just after impact, we can use the following formula:
Impulse = (Change in Momentum) = (Mass of the object) * (Change in Velocity)
Given:
Impulse (J) = 3.2 N*s
Mass (m) = 0.25 kg
As the ball is initially stationary, the initial velocity is 0 m/s.
Let's assume the final velocity of the ball as v (in m/s).
Using the formula for impulse, we have:
J = m * (v - u)
where u is the initial velocity.
Substituting the given values and rearranging the equation, we get:
3.2 = 0.25 * (v - 0)
3.2 = 0.25v
Solving the equation for v:
v = 3.2 / 0.25
v = 12.8 m/s
Therefore, the speed of the ball just after impact is 12.8 m/s.
To find the speed of the ball just after the impact, we can use the principle of conservation of momentum.
The momentum before the impact is zero because the ball is stationary.
Momentum (p) is defined as the product of an object's mass (m) and its velocity (v). Mathematically, momentum can be expressed as p = m * v.
The impulse (J) applied to an object is equal to the change in momentum it experiences. Mathematically, impulse can be expressed as J = Δp = m * Δv, where Δv is the change in velocity.
In this case, the impulse applied to the ball is given as 3.2 N*s, and the mass of the ball is 0.25 kg.
Using the formula for impulse, we can find the change in velocity:
J = m * Δv
Δv = J / m
Δv = 3.2 N*s / 0.25 kg
Δv = 12.8 m/s
Now we know the change in velocity after the impact, but we need to calculate the final velocity.
Since the initial velocity of the ball was zero, the final velocity will be equal to the change in velocity.
Therefore, the speed (v) of the ball just after the impact is 12.8 m/s.