A coach is hitting pop flies to the outfielders. If the baseball (mass=145 g) stays in contact with the bat for 0.04 s and leaves the bat with a speed of 79 m/s, what is the average force actions on the ball?
V = Vo + a*t.
78 = 0 + a*0.04, a = 1950 m/s^2,
F = M*a = 0.145 * 1950 = 283 N.
Well, you know what they say: "When the coach hits pop flies, it's always a hit or a miss-ter!" Now, let's calculate that average force.
To find the average force, you need to use Newton's second law, which states that force (F) is equal to the change in momentum (Δp) divided by the change in time (Δt).
Given that the mass of the baseball (m) is 145 g (or 0.145 kg), the initial velocity (v₁) is zero (since it starts from rest), and the final velocity (v₂) is 79 m/s, we can calculate the change in momentum using the formula:
Δp = m * (v₂ - v₁)
Δp = 0.145 kg * (79 m/s - 0 m/s)
Now, since the ball stays in contact with the bat for 0.04 s, we can substitute the values into the formula to find the average force:
F = Δp / Δt
F = (0.145 kg * (79 m/s - 0 m/s)) / 0.04 s
Solving that equation will give you the average force exerted on the ball. Just be careful not to get hit in the outfield while doing the math!
To find the average force exerted on the ball, you can use the impulse-momentum principle.
Step 1: Identify the given values:
- Mass of the baseball (m) = 145 g = 0.145 kg
- Contact time with the bat (Δt) = 0.04 s
- Final velocity of the ball (v) = 79 m/s
Step 2: Calculate the change in momentum:
Impulse (J) = Change in momentum (Δp) = m * Δv
Where m is the mass of the ball and Δv is the change in velocity.
Δp = 0.145 kg * 79 m/s
Step 3: Calculate the average force:
Average force (F) = Δp / Δt
Where Δp is the change in momentum and Δt is the contact time.
F = (0.145 kg * 79 m/s) / 0.04 s
You can now calculate the average force by substituting the given values into the formula.
To find the average force acting on the ball, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration.
First, we need to find the acceleration of the ball. We can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, the final velocity is 79 m/s, the initial velocity is 0 m/s (since the ball starts from rest on the bat), and the time is 0.04 s.
Using the formula v = u + at and solving for a:
79 m/s = 0 + a * 0.04 s
a = 79 m/s / 0.04 s
a = 1975 m/s²
Now that we have the acceleration, we can find the force. Newton's second law of motion states that force (F) is equal to mass (m) multiplied by acceleration (a).
F = m * a
F = 0.145 kg * 1975 m/s²
Now we need to convert the mass of the ball from grams to kilograms by dividing by 1000:
F = 0.145 kg * 1975 m/s²
F = 285.875 N
Therefore, the average force acting on the ball is approximately 285.875 Newtons.