During a soccer game a ball (of mass 0.425 kg), which is initially at rest, is kicked by one of the players. The ball moves off at a speed of 26 m/s. Given that the impact lasted for 8.0 ms, what was the average force exerted on the ball? Show the solution and answer.
Correction: a = (26-0)/0.008 = 3250m/s^2
Well, well, well, let's see what we got here. A ball being kicked, huh? Sounds like a real thriller! Alright, let me put on my thinking cap and calculate the average force for you.
Now, we know the mass of the ball is 0.425 kg and it starts at rest. Then, it gets kicked and moves off with a speed of 26 m/s. To find the average force, we need to use Newton's second law, which says force equals mass times acceleration.
The change in velocity over time gives us the acceleration. So, the change in velocity is given by:
(change in v) = final velocity - initial velocity
(change in v) = 26 m/s - 0 m/s
(change in v) = 26 m/s
But wait, we need to convert the impact time to seconds, so 8.0 ms should be written as 0.008 s. Don't let the tiny milliseconds fool you!
Now, let's calculate the acceleration:
acceleration = (change in v) / (change in t)
acceleration = 26 m/s / 0.008 s
acceleration = 3250 m/s²
Alright, now we can find the average force:
force = mass × acceleration
force = 0.425 kg × 3250 m/s²
force = 1381.25 N
So, drumroll please...the average force exerted on the ball is approximately 1381.25 Newtons. That's quite a kick! Don't be surprised if the ball ends up in the next county!
a = (V-Vo)/t = (0-26)/0.008s = 3250m/s^2
F = m*a = 0.425 * 3250 = 1381.3 N.
To find the average force exerted on the ball, we can use Newton's second law of motion, which states that force (F) is equal to the change in momentum (Δp) divided by the change in time (Δt).
The momentum of an object is calculated by multiplying its mass (m) by its velocity (v). In this case, the ball has a mass of 0.425 kg and moves off with a velocity of 26 m/s.
Step 1: Calculate the initial momentum (p1) and final momentum (p2) of the ball.
p1 = m * v
= 0.425 kg * 0 m/s
= 0 kg·m/s
p2 = m * v
= 0.425 kg * 26 m/s
= 11.05 kg·m/s
Step 2: Calculate the change in momentum (Δp).
Δp = p2 - p1
= 11.05 kg·m/s - 0 kg·m/s
= 11.05 kg·m/s
Step 3: Convert the impact duration from milliseconds to seconds.
Δt = 8.0 ms / 1000 ms/s
= 0.008 s
Step 4: Calculate the average force (F) exerted on the ball.
F = Δp / Δt
= 11.05 kg·m/s / 0.008 s
= 1381.25 N
Therefore, the average force exerted on the ball during the impact is 1381.25 newtons (N).
To find the average force exerted on the ball, we can use Newton's second law of motion, which states that the force acting on an object is equal to the rate of change of its momentum.
The momentum of an object is the product of its mass and velocity: p = m * v.
In this case, the ball's mass is given (m = 0.425 kg) and its initial velocity is zero (since it's at rest). After being kicked, the ball moves off with a speed of 26 m/s.
The change in momentum (∆p) is given by: ∆p = m * ∆v, where ∆v is the change in velocity.
We can find ∆v by subtracting the initial velocity (0 m/s) from the final velocity (26 m/s): ∆v = 26 m/s - 0 m/s = 26 m/s.
Now, we can calculate the change in momentum: ∆p = m * ∆v = 0.425 kg * 26 m/s = 11.05 kg·m/s.
Since the impact lasted for 8.0 ms, we need to convert the time interval into seconds: t = 8.0 ms = 8.0 * 10^(-3) s.
The average force (F_avg) exerted on the ball can be obtained by dividing the change in momentum (∆p) by the time interval (t):
F_avg = ∆p / t = 11.05 kg·m/s / 8.0 * 10^(-3) s = 1381.25 N.
Therefore, the average force exerted on the ball during the impact was 1381.25 N.