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. If the acceleration is 0.210 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 solve this problem, 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.
(a) To find the mass of the airplane, we can rearrange the equation to solve for mass:
Force = mass × acceleration
mass = Force / acceleration
Given:
Force exerted by the tractor on the pavement (F) = 1.75 * 10^4 N
Total resistance force (R) = 2400 N
Acceleration (a) = 0.210 m/s^2
Since the tractor exerts a force backward on the pavement, the total force acting on the system is:
Total force (T) = Force - R
Substituting the given values:
T = 1.75 * 10^4 N - 2400 N
T = 1.51 * 10^4 N
Now we can calculate the mass of the airplane:
mass (m) = T / a
mass = 1.51 * 10^4 N / 0.210 m/s^2
mass ≈ 7.19 * 10^4 kg
Therefore, the mass of the airplane is approximately 7.19 * 10^4 kg.
(b) To calculate the force exerted by the tractor on the airplane, we can use the equation:
Force = mass * acceleration
Given:
Friction force experienced by the airplane (A) = 2100 N
Substituting the values:
Force = mass * acceleration
2100 N = mass * 0.210 m/s^2
Now we can solve for mass:
mass = 2100 N / 0.210 m/s^2
mass = 10^4 kg
Now substituting mass in the force equation:
Force = 10^4 kg * 0.210 m/s^2
Force = 2100 N
Therefore, the force exerted by the tractor on the airplane is 2100 N.
To find the mass of the airplane, we'll use Newton's second law of motion, which states that the force acting on an object is equal to the product of its mass and acceleration:
F = ma, where F is the force, m is the mass, and a is the acceleration.
In this case, we are given the following values:
Force exerted by the tractor on the pavement (F) = 1.75 x 10^4 N (backward)
Total resistance force (Fr) = 2400 N
Acceleration (a) = 0.210 m/s^2
First, let's find the net force acting on the system:
Net force (Fnet) = F - Fr
Substituting the given values into the equation:
Fnet = 1.75 x 10^4 N - 2400 N
Fnet = 1.51 x 10^4 N
Now, we can find the mass of the airplane:
Fnet = ma
Rearranging the equation to solve for mass (m):
m = Fnet / a
Substituting the known values:
m = 1.51 x 10^4 N / 0.210 m/s^2
m ≈ 7.19 x 10^4 kg
Therefore, the mass of the airplane is approximately 7.19 x 10^4 kg.
Now, let's move on to calculating the force exerted by the tractor on the airplane.
We are given:
Friction experienced by the airplane (Fr') = 2100 N
To find the force exerted by the tractor on the airplane, we'll use the same equation as before:
F = ma
Rearranging the equation to solve for force (F):
F = ma
Substituting the known values:
F = (mass of the airplane) x a
F = (7.19 x 10^4 kg) x (0.210 m/s^2)
F ≈ 1.51 x 10^4 N
Therefore, the force exerted by the tractor on the airplane is approximately 1.51 x 10^4 N.
b. Fap-2100 = m*a
Fap-2100 = 71,905*0.21
Fap-2100 = 15,100
Fap = 17,200 N.
Fap = 17,500 N. = Force applied.
Fk = 2400 N. = Force of kinetic friction
a. m=(Fap-Fk)/a
m = (17,500-2400)/0.21=71,905 kg.