Question

What force must be applied to a body through a distance of 10m, such that it does a work of 4000J. If the mass of the body is 20kg, what is the acceleration of the bbody?

Answer 1

Answer:

• Force will be 400 Newton .
• Acceleration will be 20m/s².

Explanation:

According to the Question

Firstly we calculate the Force applied to a body .

As it is given that,

• Work Done ,W = 4000 J
• Displacement ,s = 10m

For calculating the Force applied we will use here formula

• Work Done = Force × Displacement

by putting the value we get

↠ 4000 = F × 10

↠ F = 4000/10

↠ F = 400N

• Hence, the force applied to a body will be 400 Newton .

Now , calculating the acceleration of the body .

As we know the relationship between Force , Acceleration and mass.

• Force = Mass × Acceleration

by putting the value we get

↠ 400 = 20 × Acceleration

↠ Acceleration = 400/20

↠ Acceleration = 20m/s²

• Hence, the acceleration of the body will be 20m/s².

Answer 2

Answer:

Given :-

• A body through a distance of 10 m, such that it does a work of 4000 J.
• The mass of the body is 20 kg.

To Find :-

• What is the force.
• What is the acceleration of the body.

Formula Used :-

$\clubsuit$ Work Done Formula :

$\longrightarrow \sf\boxed{\bold{\pink{Work\: Done =\: Fs}}}$

where,

• F = Force
• s = Displacement

$\clubsuit$ Force Formula :

$\longrightarrow \sf\boxed{\bold{\pink{F =\: ma}}}$

where,

• F = Force
• m = Mass
• a = Acceleration

Solution :-

First, we have to find the force :-

Given :

• Work Done = 4000 J
• Displacement = 10 m

According to the question by using the formula we get,

$\leadsto \bf Work\: Done =\: Force \times Displacement$

$\leadsto \sf 4000 =\: Force \times 10$

$\leadsto \sf \dfrac{400\cancel{0}}{1\cancel{0}} =\: Force$

$\leadsto \sf \dfrac{400}{1} =\: Force$

$\leadsto \sf 400 =\: Force$

$\leadsto \sf\bold{\red{Force =\: 400\: N}}$

$\therefore$ The force applied to a body is 400 N .

Now, we have to find the acceleration of the body :-

Given :

• Force = 400 N
• Mass = 20 kg

According to the question by using the formula we get,

$\dashrightarrow \bf Force =\: Mass \times Acceleration$

$\dashrightarrow \sf 400 =\: 20 \times Acceleration$

$\dashrightarrow \sf \dfrac{40\cancel{0}}{2\cancel{0}} =\: Acceleration$

$\dashrightarrow \sf \dfrac{40}{2} =\: Acceleration$

$\dashrightarrow \sf 20 =\: Acceleration$

$\dashrightarrow \sf\bold{\red{Acceleration =\: 20\: m/s^2}}$

$\therefore$ The acceleration of the body is 20 m/s² .