Question

The weight of a bicyclist and bicycle together is 51.0kg how much work has been done if the bicyclist slows down the bicycle from a seed of 3.95 m/s to 1.31 m/s

Answer 1

The work done is 354.1032 Joules

Step-by-step explanation:

To answer the question we note that the amount of work done is equivalent to the reduction in the kinetic energy of the bicyclist and bicycle.

Therefore, initial kinetic energy. KE
`_i` of the system is given by the following relation;

`KE_i=(1)/(2) mv_(1)^(2)`

Final kinetic energy
`KE_f = (1)/(2) mv_(2)^(2)`

Where:

v₁ = Initial velocity = 3.95 m/s

v₂ = Final velocity = 1.31 m/s

m = Mass of the bicyclist and bicycle = 51.0 kg

Change in kinetic energy ΔKE;

`\Delta KE = KE_f - KE_i`

`\Delta KE =(1)/(2) mv_(2)^(2)-(1)/(2) mv_(1)^(2) = (1)/(2) m(v_(2)^(2)-v_(1)^(2)) = (1)/(2) * 51 * (1.31^(2)-3.95^(2)) = -354.1032 \ J`

Therefore, work done = -ΔKE = 354.1032 Joules.