During a neighborhood baseball game in a vacant lot, a particularly wild hit sends a 148-g baseball crashing through the pane of a second-floor window in a nearby building. The ball strikes the glass at 10.1 m/s, shatters the glass as it passes through, and leaves the window at 8.95 m/s with no change of direction. Calculate the magnitude of this impulse.
And,
he ball is in contact with the glass for 10.1 ms as it passes through. Find the magnitude of the average force of the glass on the ball (a positive number).
Well, it seems like this baseball player has quite the talent for breaking windows! Let's calculate the magnitude of the impulse and the average force.
To calculate the magnitude of the impulse, we can use the equation:
Impulse = Change in momentum
First, let's find the change in momentum of the baseball. The momentum before the collision is given by the product of the mass and initial velocity:
Initial momentum = mass * initial velocity
= 148 g * 10.1 m/s
Next, let's find the momentum after the collision, which is also the final momentum:
Final momentum = mass * final velocity
= 148 g * 8.95 m/s
Now, we can calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
Finally, the magnitude of the impulse is simply the absolute value of the change in momentum.
For the second part of the question, to find the magnitude of the average force of the glass on the ball, we can use the equation:
Average force = Impulse / Time of contact
Given that the time of contact is 10.1 ms, we can convert it to seconds. Then we'll divide the impulse by the time of contact.
Alright, now let's crunch some numbers and find those answers!
To find the magnitude of the impulse, we can use the formula:
Impulse = Change in momentum
The momentum of an object is given by the equation:
Momentum = Mass x Velocity
Given information:
Mass of the baseball, m = 148 g = 0.148 kg
Initial velocity, u = 10.1 m/s
Final velocity, v = 8.95 m/s
First, we need to find the change in momentum:
Δmomentum = (Final momentum) - (Initial momentum)
Initial momentum = Mass x Initial velocity = m x u
Final momentum = Mass x Final velocity = m x v
Substituting the given values:
Initial momentum = 0.148 kg x 10.1 m/s
Final momentum = 0.148 kg x 8.95 m/s
Now we can calculate the change in momentum:
Δmomentum = Final momentum - Initial momentum
Finally, we can calculate the magnitude of the impulse:
Magnitude of impulse = | change in momentum |
To find the average force exerted by the glass on the ball, we can use the formula:
Force = Impulse / Time of contact
Given information:
Time of contact, t = 10.1 ms = 10.1 x 10^(-3) s
Substituting the values:
Force = Magnitude of impulse / Time of contact
Now we can solve for the magnitude of the impulse and average force.
To calculate the magnitude of the impulse, we need to use the concept of impulse-momentum theorem, which states that the impulse experienced by an object is equal to the change in momentum of the object.
Impulse (J) = Change in Momentum (Δp)
Here, the impulse is the force experienced by the ball as it passes through the window and changes its momentum.
To find the magnitude of the impulse, we first need to determine the initial momentum (p_initial) and the final momentum (p_final) of the ball.
The momentum (p) of an object is given by the equation:
p = mass (m) × velocity (v)
Given data:
Mass of the ball (m) = 148 g = 0.148 kg
Initial velocity of the ball (v_initial) = 10.1 m/s
Final velocity of the ball (v_final) = 8.95 m/s
Since the direction does not change, we only need to consider the magnitudes of velocity values.
1. Calculate the initial momentum (p_initial):
p_initial = m × v_initial
p_initial = 0.148 kg × 10.1 m/s
2. Calculate the final momentum (p_final):
p_final = m × v_final
p_final = 0.148 kg × 8.95 m/s
3. Calculate the change in momentum (Δp):
Δp = p_final - p_initial
Δp = (0.148 kg × 8.95 m/s) - (0.148 kg × 10.1 m/s)
Now, we can calculate the magnitude of the impulse by taking the absolute value of the change in momentum:
Magnitude of impulse = |Δp|
Therefore, the magnitude of the impulse can be calculated using the given data and the above steps.
Δp=FΔt
Δp= mv₂-(-mv₁)= m(v₂+v₁),
m(v₂+v₁)=FΔt
F= m(v₂+v₁)/Δt=
=0.148•(10.1+8.95)/10.1•10⁻³=132.6 N