a 900 N running back moving at 2.0 m/s is stoppped in 0.70 seconds when hit by a lineback. What average foarce did the linebacker exert on the running back?
How much did the running back's momentum change?
F = m*a
900N = m*(9.8m/s^2)
m = 91.8367 kg
a = (change in velocity) / (change in time)
a = (Vf - Vi) / (change in time)
a = (2 - 0) / (.7) = 2.85714 m/s^2
F = 91.8367 kg * 2.8571 m/s^2 = 262.391 N
change in momentum:
p = m*(change in velocity)
p = 91.8367 kg * (2 m/s) = 183.673 kg*m/s
Well, it seems we have a classic case of a linebacker putting the brakes on a running back! Let's calculate the average force the linebacker exerted on the poor fella.
Now, we know the initial velocity of the running back is 2.0 m/s, and he comes to a stop in 0.70 seconds. So, we can use the formula:
Force = (Change in momentum) / Time
The change in momentum can be calculated as:
Change in momentum = (Final momentum) - (Initial momentum)
Now, let's calculate the initial momentum of the running back:
Initial momentum = mass * initial velocity
We're given that the running back has a mass of 900 N, which is basically his weight. So, we can say that his mass is 900 N / (acceleration due to gravity).
Now, the final momentum would be zero since he comes to a stop. So, the change in momentum would just be -initial momentum.
Finally, we can calculate the average force exerted by the linebacker:
Force = (Change in momentum) / Time
So, what's the punchline? Let's find out!
To find the average force exerted by the linebacker on the running back, we can use Newton's second law of motion, which states that force is equal to the rate of change of momentum. The formula can be written as:
F = Δp / Δt
Where:
F is the average force exerted by the linebacker on the running back
Δp is the change in momentum
Δt is the time interval
First, let's calculate the change in momentum:
Δp = m * Δv
Where:
m is the mass of the running back
Δv is the change in velocity
Given:
mass of the running back, m = unknown
initial velocity, v1 = 2.0 m/s
final velocity, v2 = 0 m/s
Since the running back is stopped, the final velocity is 0. We can substitute these values into the equation:
Δv = v2 - v1
Δv = 0 - 2.0 m/s
Δv = -2.0 m/s
Now, let's consider the equation:
F = Δp / Δt
We are given the time interval, Δt = 0.70 seconds.
Since the mass of the running back (m) is unknown, we cannot calculate the exact force. However, we can still solve the problem by rearranging the equation:
F = Δp / Δt
F = m * Δv / Δt
Now, all we have to do is plug in the known values:
F = m * Δv / Δt
F = m * (-2.0 m/s) / 0.70 s
Although we don't know the mass of the running back, we can calculate the ratio of force to mass. This ratio is called acceleration (a), given by Newton's second law:
F = m * a
Rearranging this equation, we get:
a = F / m
Thus, the average force (F) exerted by the linebacker on the running back is directly proportional to the acceleration. The exact value of the force will depend on the mass of the running back.
To find the average force exerted by the linebacker, 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.
First, we need to find the initial momentum (p1) of the running back before being stopped. Momentum (p) is calculated by multiplying the mass (m) of an object by its velocity (v). However, the mass is not given in this question, so we will need to use the formula for force (F) instead.
The formula for force is given by F = m * a, where F is the force, m is the mass, and a is the acceleration.
The acceleration can be found using the second equation of motion, s = ut + (1/2)at^2, where s is the displacement, u is the initial velocity, t is the time, and a is the acceleration.
Rearranging the equation to solve for acceleration, we have a = (2s - 2ut) / t^2.
Since the running back is being stopped, the final velocity (v) is 0, so the displacement (s) can be calculated as s = (1/2)(u + v)t.
Plugging in the given values, we have:
s = (1/2)(2.0 m/s + 0)(0.70 s) = 0.70 m.
Now we can calculate the acceleration:
a = (2(0.70 m) - 2(2.0 m/s)(0.70 s)) / (0.70 s)^2 ≈ -9.80 m/s^2. (Note: The negative sign indicates deceleration.)
Next, we can find the mass using the formula for force:
F = m * a => 900 N = m * (-9.80 m/s^2).
Solving for m, we get m = 900 N / (-9.80 m/s^2) ≈ -91.84 kg.
Now that we have the mass (m) and the initial velocity (u), we can calculate the initial momentum (p1):
p1 = m * u = (-91.84 kg)(2.0 m/s) ≈ -183.68 kg·m/s.
The final momentum (p2) is 0 kg·m/s because the running back comes to a stop.
The change in momentum (Δp) is given by Δp = p2 - p1 = 0 - (-183.68 kg·m/s) = 183.68 kg·m/s.
Therefore, the running back's momentum changed by 183.68 kg·m/s.
As for the average force exerted by the linebacker, we can use the formula F = Δp / Δt, where F is the force, Δp is the change in momentum, and Δt is the change in time.
The change in time (Δt) is given as 0.70 seconds.
Plugging in the given values, we have:
F = (183.68 kg·m/s) / (0.70 s) ≈ 262.40 N.
Therefore, the average force exerted by the linebacker on the running back is approximately 262.40 Newtons.