Question

A force of 10n acts for 20second on a body of mass2 kg initially at rest calculate the energy required by the body and the work done by the applied force

Answer 1

An alternative would be to use work energy theorem at the last step in which you can equate work done to difference in kinetic energies.

W = Kf - Ki

but, Ki = 0

So, W = Kf = 10^4J

Do refer to the attachment for the rest of the solution.

Answer 2

Provided that:

• Force = 10 Newton
• Time taken = 20 seconds
• Mass = 2 kilograms
• Initial velocity = 0 m/s

To calculate:

• The energy
• Work done

Solution:

• The energy = 10000 J
• Work done = 10000 J

Using concepts:

• Work-energy theorm
• Kinetic energy formula
• Force formula
• First equation of motion
• Power formula
• Energy formula

Using formulas:

• According to work-energy theorm,

• ${\small{\underline{\boxed{\sf{W \: = K.E_v \: - K.E_u}}}}}$

• Kinetic energy is given by,

• ${\small{\underline{\boxed{\sf{K.E \: = \dfrac{1}{2} \: mv^2}}}}}$

• Force formula is mentioned below,

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

• First equation of motion is below,

• ${\small{\underline{\boxed{\sf{v \: = u \: + at}}}}}$

• Power is given by,

• ${\small{\underline{\boxed{\sf{P \: = \dfrac{W}{t}}}}}}$

• Energy is given by,

• ${\small{\underline{\boxed{\sf{E \: = P \times t}}}}}$

Where, W denotes work done, K.E_v denotes final kinetic energy, K.E_u denotes initial kinetic energy, F denotes force, m denotes mass, a denotes acceleration, v denotes final velocity, u denotes initial velocity, t denotes time, P denotes power, E denotes energy and K.E denotes kinetic energy.

Required solution:

~ Firstly let us calculate acceleration by using formula to calculate force!

$:\implies \sf Force \: = Mass \times Acceleration \\ \\ :\implies \sf F \: = m \times a \\ \\ :\implies \sf F \: = ma \\ \\ :\implies \sf 10 = 2(a) \\ \\ :\implies \sf 10 = 2 \times a \\ \\ :\implies \sf \dfrac{10}{2} \: = a \\ \\ :\implies \sf 5 \: = a \\ \\ :\implies \sf a \: = 5 \: ms^{-2} \\ \\ :\implies \sf Acceleration \: = 5 \: ms^{-2}$

Acceleration = 5 metre per second sq.

~ Now let's calculate final velocity by using first equation of motion!

$:\implies \sf v \: = u \: + at \\ \\ :\implies \sf v \: = 0 + 5(20) \\ \\ :\implies \sf v \: = 0 + 100 \\ \\ :\implies \sf v \: = 100 \: ms^{-1} \\ \\ :\implies \sf Final \: velocity \: = 100 \: ms^{-1}$

Final velocity = 100 metre per second

~ Now let's calculate the work done by using the work-energy theorm!

$:\implies \sf Work \: done \: = Change \: in \: kinetic \: energy \\ \\ :\implies \sf W \: = K.E_v \: - K.E_u \\ \\ :\implies \sf W \: = \dfrac{1}{2} \: mv^2 - \dfrac{1}{2} \: mu^2 \\ \\ :\implies \sf W \: = \dfrac{1}{2} \times 2 \times 100 \times 100 - \dfrac{1}{2} \times 2 \times 0 \times 0 \\ \\ :\implies \sf W \: = \dfrac{1}{2} \times 2 \times 10000 - \dfrac{1}{2} \times 2 \times 0 \\ \\ :\implies \sf W \: = \dfrac{1}{2} \times 20000 - \dfrac{1}{2} \times 0 \\ \\ :\implies \sf W \: = 10000 - 0 \\ \\ :\implies \sf W \: = 10000 \: J \\ \\ :\implies \sf Work \: done \: = 10000 \: Joules$

Work done = 10,000 J

~ Now by using power formula let's find out the power!

$:\implies \sf P \: = \dfrac{W}{t} \\ \\ :\implies \sf Power \: = \dfrac{Work \: done}{Time} \\ \\ :\implies \sf Power \: = \dfrac{10000}{20} \\ \\ :\implies \sf Power \: = \dfrac{1000}{2} \\ \\ :\implies \sf Power \: = 500 \: Watts$

Power = 500 Watts

~ Now finding energy!

$:\implies \sf E \: = P \times t \\ \\ :\implies \sf Energy \: = Power \times Time \\ \\ :\implies \sf Energy \: = 500 \times 20 \\ \\ :\implies \sf Energy \: = 10000 \: Joules$

Energy = 10,000 Joules