Question

A particle of mass m is driven by a machine that delivers constant power k watts . If the particle starts from rest the force on particle at time t is

Answer 1

Answer:

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Explanation:

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Answer 2

Dear student,

Given :-

• mass of particle = m
• constant power = k watt
• initial velocity = 0

To find :-

• force on the particle at time t

Solution :-

We know by the formula of power that;

              P = F.v

Putting the given values in the formula, we get;

            k = F.v

            k = ma.v

            k = m dv/dt . v

      ∫k dt = m ∫v dv

          kt = m[v²/2]

          kt = mv²/ 2

          v² = 2 kt/ m

           v = √2kt/ m

   dv/ dt = d(√2kt/ m)/ dt

          a = 1/2 √2k/mt

We know for force, that;

           F = ma

Putting the obtained and given values in the above formula, we obtain;

           F = m × 1/2 √2k/mt

          F = √mk/2t

Hence, the force on the particle at time t is √mk/2t  N.