Question

A catapult on an aircraft carrier is capable of accelerating a plane from 0 to 56 m/s in a distance of 80 m. Find the average net force that the catapult exerts on a 13300 kg jet.​

Answer 1

Answer :-

Average net force exerted by the catapult on the jet is 260.68 kN .

Explanation :-

We have :-

→ Initial velocity of the plane = 0 m/s

→ Final velocity of the plane = 56 m/s

→ Distance = 80 m

→ Mass of the plane = 13300 kg

______________________________

Firstly, let's calculate acceleration of the plane by using the 3rd equation of motion :-

v² - u² = 2as

⇒ (56)² - 0 = 2(a)(80)

⇒ 3136 = 160a

⇒ a = 3136/160

⇒ a = 19.6 m/s²

∴ Acceleration of the plane = 19.6 m/s²

______________________________

Now, according to Newton's 2nd law of motion :-

F = ma

⇒ F = 13300 × 19.6

⇒ F = 260680 N

⇒ F = 260.68 kN

Answer 2

${\large{\pmb{\sf{\underline{RequirEd \: solution...}}}}}$

${\bigstar \:{\pmb{\sf{\underline{About \: question...}}}}}$

⋆ Understanding the question: This question says that we have to find out the average net force that the catapult exerts on a 13300 kilograms jet. Given that there is a catapult on an aircraft and it is capable of accelerating a plane from 0 to 56 m/s in a distance of 80 m. Let's do it!

${\bigstar \:{\pmb{\sf{\underline{Provided \: that...}}}}}$

$\sf According \: to \: statement \begin{cases} & \sf{Initial \: velocity \: = \bf{0 \: m/s}} \\ \\ & \sf{Final \: velocity \: = \bf{56 \: m/s}} \\ \\ & \sf{Distance \: = \bf{80 \: metres}} \\ \\ & \sf{Mass \: of \: body \: = \bf{13300 \: kilograms}} \\ \\ & \sf{Average \: net \: force \: = \bf{?}} \end{cases}$

${\bigstar \:{\pmb{\sf{\underline{Using \: concepts...}}}}}$

⋆ Third equation of motion is given by the mentioned formula:

${\small{\underline{\boxed{\sf{2as \: = v^2 - u^2}}}}}$

• (Where, a denotes acceleration , s denotes displacement or distance , v denotes final velocity and u denotes initial velocity)

⋆ Newton's second law of motion formula that is of force is given by:

${\small{\underline{\boxed{\sf{F \: = ma}}}}}$

• (Where, F denotes force , m denotes mass of body and a denotes acceleration)

${\bigstar \:{\pmb{\sf{\underline{Full \; Solution...}}}}}$

~ Firstly by using third equation of motion let us find out the acceleration!

$:\implies \sf 2as \: = v^2 - u^2 \\ \\ :\implies \sf 2a(80) = (56)^{2} - 0^{2} \\ \\ :\implies \sf 2a(80) = 3136 - 0 \\ \\ :\implies \sf 2(a)(80) = 3136 \\ \\ :\implies \sf 2(80a) = 3136 \\ \\ :\implies \sf 160a = 3136 \\ \\ :\implies \sf a = 3136/160 \\ \\ :\implies \sf a = 19.6 \: ms^{-2}$

Henceforth, we get 19.6 m/s sq. as the acceleration.

~ Now by using Newton's second law of motion formula that is of force, let us solve the whole question!

$:\implies \sf F \: = ma \\ \\ :\implies \sf F \: = 13300(19.6) \\ \\ :\implies \sf F \: = 13300 \times 19.6 \\ \\ :\implies \sf F \: = 260680.0 \: Newton \\ \\ :\implies \sf Average \: net \: force \: = 260.68 \: kN$

Henceforth, we get 260.68 kN as average net force.

${\large{\pmb{\sf{\underline{AdditioNal \: Knowledge...}}}}}$

➟ Newton's law of motion -Newton if the father of physics and he established the laws of motion in his book named ❛Principia❜ in the year 1667.

➟ Newton's first law of motion - Every body maintain it's maintain it's initial state of rest or motion with uniform speed on straight line unless an external force act on it.

◆ It's also known to be law of Galileo or law of inertia.

• Law of inertia = It is the property of a body by virtue of which the body opposes change in it's initial state of rest or motion with uniform speed on a straight line. There are 2 types of inertia –

⑴ Inertia of rest

⑵ Inertia of motion

Some examples of inertia –

⑴ When a coat /blanket is beaten by a stick the dust particles are removed.

⑵ When a car start suddenly the passenger bends backwards.

◆ Important - First law gives the definition of force.

• Force - It is that external cause which when acts on a body changes or tries to change the initial state of the body.

• Momentum - It is that property of a moving body and is defined of mass and velocity of the body. It's a vector quantity. SI unit is kgm/s.

$\: \: \: \: \: \: \:{\sf{Momentum = \: Mass \times Velocity}} \: \: \green\star$

➟ Newton's 2nd law of motion - The rate of change in momentum of a body is directly proportional to the applied force on the body and take place in the direction of force.

If f = force applied ; a = acceleration produced and m = mass of body the nF = ma.

◆ Newton's second law gives the magnitude of force.

◆ Newton's first law is contained in the second law.

➟ Newton's 3rd law of motion - To every action there is an equal and opposite reaction.

Some examples -

⑴ Motion of the rocket.

⑵ Recoil of the gun.