Work and force (my answers keep being wrong please someone explain)

[bubba640]

A plane weighing 220 kN (25 tons) lands on an aircraft carrier. The plane is moving horizontally at 62 m/s (139 mi/h) when its tailhook grabs hold of the arresting cables. The cables bring the plane to a stop in a distance of 88 m.
(a) How much work is done on the plane by the arresting cables?
MJ

(b) What is the force (assumed constant) exerted on the plane by the cables?
kN opposite the plane's direction of motion

(Note: Both answers will be underestimates, since the plane lands with the engines full throttle forward; in case the tailhook fails to grab hold of the cables, the pilot must be ready for immediate takeoff.)

how to do it

mass of the plane m = m kg
given velocity of the plane be = v m/sec
initial kinetic energy of the plane
K = mv^2 / 2
the work done by the cables in bringing the plane to rest
W = K
the force excerted by the cables
F = W / S
where S is the disatance over which the plane brought to rest .


My Work

first I converted kN to Kg by multiplying 220 kN by 101.97 kg= 22433.4 kg

then
KE= (22433.4kg)(62m/s)^2 / 2= 43116994.8

W=K but my answer was wrong

and then

43116994.8/88= 489965.85 which also was wrong

PLEASE EXPLAIN

 

[s8wardwe]

Check your unit conversions. I believe your error exists there. Remember Force is mass times the acceleration due to gravity. This mass you will need to find the kinetic energy.

 

[baba89]

I can provide a more detailed explanation of how to solve this problem. First, let's define the variables given in the problem:
- Mass of the plane (m): 220 kN or 22433.4 kg
- Initial velocity of the plane (v): 62 m/s
- Distance over which the plane is brought to rest (S): 88 m
- Force exerted by the cables (F): unknown

To solve for the work done by the cables, we can use the formula W = F * S, where W is the work, F is the force, and S is the distance. However, we do not know the force yet, so we need to solve for it first.

To find the force exerted by the cables, we can use the formula F = ma, where F is the force, m is the mass, and a is the acceleration. In this case, the acceleration is the change in velocity divided by the time it takes to change, which is the same as the initial velocity divided by the distance traveled (since the plane is brought to rest). So we can rewrite the formula as F = m * v / S. Plugging in the known values, we get:
F = (22433.4 kg) * (62 m/s) / (88 m) = 15946.3 N.
Note that this is the force exerted by the cables in the opposite direction of the plane's motion, as stated in the problem.

Now that we know the force, we can solve for the work done by the cables:
W = (15946.3 N) * (88 m) = 1.403 * 10^6 J, or 1.403 MJ.

To compare this to your answer, it seems like you may have used the incorrect units for mass (kg instead of kg*m/s^2) and velocity (m/s instead of m/s^2). Also, in your calculation for work, you used the incorrect formula, as you should have multiplied the force by the distance, not divided. I hope this explanation helps clarify the steps needed to solve this problem.