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It's possible for a determined group of people to pull an aircraft. Drag is negligible at low speeds, and the only force impeding motion is the rolling friction of the rubber tires on the concrete runway. In 2000, a team of 60 British police officers set a world record by pulling a Boeing 747, with a mass of 200,000 kg, a distance of 100 m in 53 s. The plane started at rest. Suppose that μr=0.02.



Estimate the force with which each officer pulled on the plane, assuming constant pulling force and constant acceleration.

Respuesta :

Answer:

867 N

Explanation:

Given:

Mass of the aircraft (m) = 200,000 kg

Displacement of the aircraft (d) = 100 m

Time taken (t) = 53 s

Coefficient of friction between the tires and concrete (μ) = 0.02

Number of police officers (n) = 60

Initial velocity of aircraft (u) = 0 m/s

Now, using equation of motion, we can find the acceleration of the aircraft.

The equation of motion is given as:

[tex]d=ut+\frac{1}{2}at^2[/tex]

Here, 'a' is the acceleration of the aircraft.

Plug in the given values and solve for 'a'. This gives,

[tex]100=0+\frac{1}{2}a(53)^2\\\\a=\frac{200}{2809}= 0.07\ m/s^2[/tex]

Now, the frictional force is given as:

[tex]f=\mu N=\mu mg=0.02\times 200000\times 9.8=39200\ N[/tex]

Now, let the force of pull of one police be 'F'.

So, the total force of pull of 60 officers = 60F

Now, the net force acting on the aircraft is given as:

[tex]F_{net}=60F-f\\\\F_{net}=60F-39200[/tex]

From Newton's second law, the net force acting on the aircraft is equal to the product of mass and acceleration. So,

[tex]F_{net}=ma\\\\60F-39200=200000\times 0.07\\\\60F=14000+39200\\\\60F=53200\\\\F=\frac{53200}{60}=866.67\approx 867\ N[/tex]

Therefore, the force with which each officer pulled on the plane is 867 N.

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