Question

An aeroplane of mass 10,000 kg requires a speed of 20 m/s for take-off , the run on the ground being 100 m. The coefficient of kinetic friction between the wheels of the plane and ground is 0.3. Assume that the plane accelerates uniformly during the take-off . Determine the minimum force required by the engine of the plane to take off. (g = 10 m/s²)​

Answer 1

Step-by-step explanation:

Required Answer :

${\bold{\red{❖ \: \: \: \: \: \: \: \: \: }}}{\bold{\rm{5 × 10⁴ \: N}}}$

Given :-

• Mass, m = 10,000 kg
• Distance, s = 100m
• Initial velocity, u = 0 m/s
• Final velocity, v = 20 m/s
• Gravitational Acceleration, a = 10 m/s²

To find :

• The minimum force required by the engine of the plane to take off.

Solution :

Let a be the acceleration of the aeroplane during it's take-off rum of 100 m, acquiring a speed of 20 m/s

Using relation v² = u² + 2as, we have

${\bold{\sf{⟼ \: \: \: \: \: (20)² \: = \: 0 \: + \: 2a(100)}}}$

${\bold{\sf{⟼ \: \: \: \: \: a \: = \: \frac{20 × 20}{2 × 100}}}}$

${\bold{\sf{⟼ \: \: \: \: \: a \: = \: \frac{400}{200}}}}$

${\bold{⟼ \: \: \: \: \: }}{\bold{\underline{\boxed{\rm{\color{magenta}{a \: = \: 2 \: m/{s}^{2}}}}}}}$

Therefore,

❥The force required for producing this acceleration is,

${\bold{\sf{⟼ \: \: \: \: \: F \: = \: ma}}}$

${\bold{\sf{⟼ \: \: \: \: \: 10,000 \: kg \: × \: 2 \: m/s²}}}$

${\bold{⟼ \: \: \: \: \: }}{\bold{\underline{\boxed{\rm{\color{magenta}{2 \: × \: 10⁴ \: N}}}}}}$

❥The minimum force required to overcome the friction during the take-off is,

${\bold{\sf{⟼ \: \: \: \: \: μ_k \: mg}}}$

${\bold{\sf{⟼ \: \: \: \: \: 0.3 \: × \: 10,000 \: kg \: × \: 10 \: m/s²}}}$

${\bold{⟼ \: \: \: \: \: }}{\bold{\underline{\boxed{\rm{\color{magenta}{3 \: × \: 10⁴ \: N}}}}}}$

❥Hence the total force required by the engine of the plane to take-off is,

${\bold{\sf{⟼ \: \: \: \: \: F \: + \: μ_k \: mg}}}$

${\bold{\sf{⟼ \: \: \: \: (2 × 10⁴) \: + \: (3 × 10⁴)}}}$

${\bold{⟼ \: \: \: \: \: }}{\bold{\underline{\boxed{\rm{\color{magenta}{5 \: × \: 10⁴ \: N}}}}}}$