A boxer is punching the heavy bag. The time of impact of the glove with the bag is 0.10 s. The mass of the glove and his hand is 3 kg. The velocity of the glove just before impact is 25 m/s. What is the average impact force exerted on the glove?
f = m a
f = 3 kg * (25 m/s / .10 s)
Well, I'm glad you're not asking me to step into the ring with a boxer. I'm more of a joker than a puncher! Anyway, let's do some math here.
To find the average impact force, we can use Newton's second law of motion, which states that force (F) equals mass (m) multiplied by acceleration (a). Since the time of impact (t) is given, we can find the acceleration using the formula: acceleration (a) equals the change in velocity (Δv) divided by the time of impact (t).
The change in velocity is the final velocity (v_f), which is 0 m/s after the impact, minus the initial velocity (v_i), which is 25 m/s before the impact. So, Δv = 0 - 25 m/s = -25 m/s.
Now we can calculate the acceleration: a = Δv / t = (-25 m/s) / 0.10 s = -250 m/s².
Since the boxer is hitting the bag, we assume that the glove comes to rest after impact, meaning the final velocity is 0 m/s. Using the equation F = m * a, where m is the mass of the glove and hand (3 kg) and a is the acceleration (-250 m/s²), we can determine the average impact force.
F = (3 kg) * (-250 m/s²) = -750 N.
Now, I didn't expect negative force, but it just means that the force is directed opposite to the motion. So, the average impact force exerted on the glove is approximately 750 Newtons. That's quite a punch!
To calculate the average impact force exerted on the glove, we can use the impulse-momentum principle. The impulse is equal to the change in momentum, which can be calculated using the formula:
Impulse = Change in momentum
The change in momentum of the glove can be calculated using the formula:
Change in momentum = Final momentum - Initial momentum
The final momentum can be calculated using the formula:
Final momentum = Mass * Final velocity
The initial momentum can be calculated using the formula:
Initial momentum = Mass * Initial velocity
The average impact force can be calculated using the formula:
Average impact force = Impulse / Time of impact
Let's calculate step by step.
1. Calculate the final momentum:
Mass = 3 kg
Final velocity = 25 m/s
Final momentum = Mass * Final velocity
= 3 kg * 25 m/s
= 75 kg·m/s
2. Calculate the initial momentum:
Initial velocity = 0 m/s
Initial momentum = Mass * Initial velocity
= 3 kg * 0 m/s
= 0 kg·m/s
3. Calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
= 75 kg·m/s - 0 kg·m/s
= 75 kg·m/s
4. Calculate the average impact force:
Time of impact = 0.10 s
Average impact force = Impulse / Time of impact
= Change in momentum / Time of impact
= 75 kg·m/s / 0.10 s
= 750 N
Therefore, the average impact force exerted on the glove is 750 Newtons.
To find the average impact force exerted on the glove, we can use Newton's second law of motion, which states that the force exerted on an object is equal to the rate of change of its momentum.
Momentum is defined as the product of an object's mass and its velocity:
Momentum (p) = mass (m) × velocity (v)
The change in momentum is equal to the final momentum minus the initial momentum:
Δp = p_f - p_i
Since we know the mass and velocity of the glove just before impact, we can calculate its initial momentum. The final momentum is zero, assuming the glove comes to a stop after impact. Therefore, the change in momentum is equal to the initial momentum:
Δp = p_i
The average impact force (F_avg) exerted on the glove is equal to the change in momentum divided by the time of impact:
F_avg = Δp / t
Let's plug in the known values:
Mass of glove and hand (m) = 3 kg
Initial velocity (v_i) = 25 m/s
Time of impact (t) = 0.10 s
First, calculate the initial momentum:
p_i = m × v_i
p_i = 3 kg × 25 m/s
p_i = 75 kg·m/s
Next, calculate the change in momentum:
Δp = p_i
Δp = 75 kg·m/s
Finally, calculate the average impact force:
F_avg = Δp / t
F_avg = 75 kg·m/s / 0.10 s
F_avg = 750 N
Therefore, the average impact force exerted on the glove is 750 Newtons.