Commercial airplanes are sometimes towed out of the passenger loading area by a tractor. The 1800 kg tractor exerts a force of 1.75 104 N backward on the pavement, and the system experiences forces resisting motion that total 2400 N.
(a) If the acceleration is 0.250 m/s2, what is the mass of the airplane?
(b) Calculate the force exerted by the tractor on the airplane, assuming 2100 N of the friction is experienced by the airplane.
To find the mass of the airplane, we can use Newton's Second Law of Motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. Rearranging this equation, we have:
Force = mass x acceleration
In this scenario, we know that the force exerted by the tractor on the pavement is 1.75 x 10^4 N and the force resisting motion is 2400 N. Therefore, the net force acting on the system is the difference between these two forces:
Net force = Force exerted by tractor - Force resisting motion
Substituting the given values, we have:
Net force = 1.75 x 10^4 N - 2400 N
Net force = 1.75 x 10^4 N - 2.4 x 10^3 N
Net force = 1.726 x 10^4 N
Now we can apply Newton's Second Law to find the mass. Rearranging the equation, we have:
mass = Net force / acceleration
Substituting the given values, we have:
mass = 1.726 x 10^4 N / 0.250 m/s^2
mass = 69,040 kg
Therefore, the mass of the airplane is 69,040 kg.
To calculate the force exerted by the tractor on the airplane, we need to account for the friction experienced by the airplane. The friction opposing motion is given as 2100 N.
Let's assume the force exerted by the tractor on the airplane is F.
Now, the net force acting on the airplane is:
Net force = Force exerted by tractor - Force resisting motion
Substituting the given values, we have:
2100 N = F - 2400 N
We rearrange the equation to solve for F:
F = 2100 N + 2400 N
F = 4500 N
Therefore, the force exerted by the tractor on the airplane is 4500 N.