Question

How much work must be done by a force on 50 kg body in order to accelerate it from rest to 20m/s in 10s

Answer 1

Answer:

The answer will be 10 KJ (kilo-joule)

Explanation:

Given data are

Initial velocity  u = 0 m/sec since its in rest initially

after  t = 10 sec the final velocity  v = 20 m/sec

Here we will use two formulas which are

v = u + at ................ (1)

v² = u² + 2as .................. (2)

where ''v'' and ''u'' are already defined above. ''S'' is the distance which is already covered; ''t'' is the time taken to cover up this distance and ''a'' is the acceleration.

so now using equation (1) and given data we can write

20 = 0 + a*10

or 10a = 20

or a = 2 m/sec²

now we know the acceleration , time and the both initial ; final velocities. Therefore by using equation (2) we can easily get the value of covered up distance ''s''

so, we can write       20² = 0² + 2*2*s

                            or  400 = 4s

                             or s = 100 m

Now we need a basic idea regarding ''work done''. Generally if a particle moves some distance due to a applied force then we can say an amount of work is done by the particle. Now this amount of work done can be expressed mathematically like this

W = F*d

where W= work done ; F= force ; d= covered up distance

we also know the relation,    Force = mass * acceleration

according to our question mass = 50 kg

and calculated acceleration = 2 m/sec²

and also covered up distance = 100 m

so F= 50*2 kg*m/sec² = 100 N

Finally work done   W = 100*100 N-m

                                or W = 10000 Joule = 10 KJ

so 10 Kilo-joule work must be done by the force.

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