A combat jet lands on a carrier with a horizontal velocity of 50 m/s. A stopping mechanism exerts a horizontal force of Tx = 10,000 V N, V, being the velocity of the jet in m/s. The mass of the jet is 6500 Kg. a.) What is the the maximum force that the mechanism exerts on the jet?
b.)What distance does the jet run before it comes to a complete halt?
To answer these questions, we need to apply Newton's second law of motion, which states that the net force exerted on an object is equal to the mass of the object multiplied by its acceleration.
a.) To find the maximum force that the mechanism exerts on the jet, we need to determine the acceleration of the jet. We can use the formula:
Fnet = m * a
where Fnet is the net force, m is the mass of the jet, and a is the acceleration.
In this case, the net force is equal to the force exerted by the stopping mechanism, which is Tx = 10,000 V N. The mass of the jet is given as 6500 kg.
So, we can rearrange the formula to solve for the acceleration:
a = Fnet / m
Let's substitute the values:
a = (10,000 V N) / (6500 kg)
To get the maximum value, we need to maximize the acceleration. We know that velocity is changing, so we can assume the jet is coming to a stop. Hence, the acceleration will have a negative sign.
Let's assume the maximum force is exerted at the end when the velocity is just about to reach 0 m/s:
V = 0 m/s
a = Fmax / m
Therefore, we have:
0 = Fmax / (6500 kg)
Solving for Fmax, we find:
Fmax = 0 N
b.) To find the distance the jet runs before coming to a complete halt, we can use the equation of motion:
v^2 = u^2 + 2as
where v is the final velocity (0 m/s), u is the initial velocity (50 m/s), a is the acceleration, and s is the distance.
We already know the initial velocity and the final velocity, so we can rearrange the equation to solve for s:
s = (v^2 - u^2) / (2a)
Substituting the values, we get:
s = (0^2 - 50^2) / (2a)
Since a is the acceleration we found in part (a), we can substitute that in as well:
s = (0^2 - 50^2) / (2 * (10,000 V N / 6500 kg))
Simplifying further, we have:
s = (-2500) / (2 * V N / 6500)
s = -(2500 * 6500) / (2 * V N)
So, the distance the jet runs before coming to a complete halt is -(2500 * 6500) / (2 * V N).