Question

An object of 40 kg mass is moving with
2 m/s velocity Now
force is
applied on
the object such that its
velocity increases upto 5m/s
Calculate the
work done by force.​

Answer 1

Answer:

420 Joules

Explanation:

Given:

• Mass of the object = 40 kg
• Initial velocity of the object = 2 m/s
• Final velocity = 5 m/s

To find:

• Work done by the force

Work-energy theorem states that the change in the kinetic energy is equal to the work done, so:

Initial kinetic energy:

$\frac{1}{2} mu^{2}$

$=\frac{1}{2} \times 40 \times 2^{2}$

$=20 \times 4$

$=80 J$

Final kinetic energy:

$\frac{1}{2} mv^{2}$

$=\frac{1}{2} \times 40 \times 5^{2}$

$=20 \times 25$

$=500 J$

Change in kinetic energy = Final kinetic energy - Initial kinetic energy

Change in kinetic energy = $500J-80J$

Change in kinetic energy = $420 \ Joules$

The work done is equal to 420 joules

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Work\:Done=420\:J}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Mass \: of \: object(m) = 40 \: kg \\ \\ \tt: \implies Initial \: velocity(u) = 2 \: m/s \\ \\ \tt: \implies Final \: velocity (v) = 5 \: m/s \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Work \: done(w) = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies {v}^{2} = {u}^{2} + 2as \\ \\ \tt: \implies {v}^{2} - {u}^{2} = 2as \\ \\ \tt: \implies s = \frac{ {v}^{2} - {u}^{2} }{2a} - - - - - (1) \\ \\ \bold{As \: we \: know \:that} \\ \tt: \implies F= Ma \\ \\ \tt: \implies F = 40 \times a \\ \\ \tt: \implies F = 40a - - - - - (2) \\ \\ \bold{For \: Work \: Done : } \\ \tt: \implies Work \: Done = Force \times Displacement \\ \\ \tt: \implies Work \: Done =40 \times a \times (\frac{ {v}^{2} - {u}^{2} }{2a}) \\ \\ \tt: \implies Work \: Done =40 \times a \times ( \frac{ {5}^{2} - {2}^{2} }{2 \times a}) \\ \\ \tt: \implies Work \: Done = 20 \times (25 - 4) \\ \\ \tt: \implies Work \: Done =20 \times 21 \\ \\ \green{\tt: \implies Work \: Done = 420 \: Joule} \\ \\ \green{\tt \therefore Work \: Done \: by \: object \: is \: 420 \: J}$