a football punter accelerates a football from rest to a speed of 7 m/s during the time in which his toe is in contact with the ball (about 0.18 s). If the football has a mass of 0.50 kg, what average force does the punter exert on the ball?
Well, it seems this punter is really kicking things up a notch! To find the average force, we can use Newton's second law, which states that the force exerted on an object is equal to its mass multiplied by its acceleration.
In this case, the punter accelerates the ball from rest to a speed of 7 m/s in 0.18 seconds. To find the acceleration, we can use the formula: acceleration = change in velocity / time elapsed.
So, the acceleration = (7 m/s - 0 m/s) / 0.18 s = 38.89 m/s² (approximately).
Now, using Newton's second law, the force exerted by the punter on the ball is given by the formula: force = mass × acceleration.
Plugging in the values, we have: force = 0.50 kg × 38.89 m/s².
Calculating that, we find that the average force exerted by the punter on the ball is approximately 19.45 N. That's one powerful punt!
To find the average force exerted by the punter on the ball, we can use Newton's second law of motion, which states that force (F) is equal to the mass (m) of the object multiplied by its acceleration (a).
1. Firstly, we need to calculate the acceleration of the football.
Given: Initial speed (u) = 0 m/s, Final speed (v) = 7 m/s, Time (t) = 0.18 s
The formula for acceleration is: a = (v - u) / t
Substitute the given values:
a = (7 m/s - 0 m/s) / 0.18 s
Simplify the equation:
a = 7 m/s / 0.18 s
a ≈ 38.89 m/s²
2. Now, we can calculate the average force exerted by the punter on the ball.
Formula: F = m * a
Given: Mass (m) = 0.50 kg, Acceleration (a) ≈ 38.89 m/s²
Substitute the values:
F = 0.50 kg * 38.89 m/s²
Evaluate the expression:
F ≈ 19.44 N
Therefore, the average force exerted by the punter on the ball is approximately 19.44 Newtons.
To find the average force exerted by the punter on the ball, we can use Newton's second law of motion, which states that force is equal to the rate of change of momentum. The momentum of an object is given by mass multiplied by velocity.
First, let's find the initial momentum and final momentum of the ball. The initial momentum (p₁) is given by the product of the mass of the ball and its initial velocity, which is zero since the ball is at rest initially:
p₁ = m * v₁ = 0.50 kg * 0 m/s = 0 kg⋅m/s
The final momentum (p₂) is given by the product of the mass of the ball and its final velocity, which is 7 m/s:
p₂ = m * v₂ = 0.50 kg * 7 m/s = 3.5 kg⋅m/s
The change in momentum (∆p) is the difference between the final and initial momentum:
∆p = p₂ - p₁ = 3.5 kg⋅m/s - 0 kg⋅m/s = 3.5 kg⋅m/s
Next, we need to calculate the time (t) in seconds for which the punter's toe is in contact with the ball:
t = 0.18 s
Now, we can calculate the average force (F) using the formula:
F = ∆p / t
Plugging in the values, we get:
F = 3.5 kg⋅m/s / 0.18 s ≈ 19.44 N
Therefore, the average force exerted by the punter on the ball is approximately 19.44 Newtons.