Question

A body of mass 500 g is moving with a speed of 10 m/s. A force acts on it which

makes it to move with a speed of 20 m/s. Find:

i. Change in KE

ii. Work done by the force on the body​

Answer 1

Answer:

$\bigstar{\bold{Change\:in\:K.E=75\:J}}$

$\bigstar{\bold{Work\:done=75\:J}}$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Mass of the body (m) = 500 g = 0.5 kg
• Initial velocity (u) = 10 m/s
• Final velocity(v) = 20 m/s

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Change in K.E
• Work done by the force on the body

$\Large{\underline{\underline{\bf{Solution:}}}}$

Change in K.E

→ First we have to find the initial and final kinetic energies.

→ The initial kinetic energy is given by

  Initial K.E = 1/2 m u²

→ Substitute the data,

   Initial K.E = 1/2 × 0.5 × 10 × 10

   Initial K.E = 0.5 × 5 × 10

   Initial K.E = 25 J

→ Hence the initial K.E of the body is 25 J

→ Now the final kinetic energy of the body is given by

  Final K.E = 1/2 × m × v²

→ Substitute the data,

  Final K.E = 1/2 × 0.5 × 20 × 20

  Final K.E = 0.5 × 10 × 20

  Final K.E = 100 J

→ Hence the final kinetic energy of the body is 100 kg m/s

→ The change in K.E is given by

   Change in K.E = Final K.E - Initial K.E

   Change in K.E = 100 - 25

   Change in K.E = 75 J

→ Hence the change in K.E is 75 J

$\boxed{\bold{Change\:in\:K.E=75\:J}}$

Work done:

→ Now we have to find the work done by the force.

→ By work energy theorem the work done is defined as the change in K.E

→ Hence,

  Work done = Change in K.E

  Work done = 75 J

→ Hence work done by the force is 75 J

$\boxed{\bold{Work\:done=75\:J}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ The kinetic energy of a body is given by

   K.E = 1/2 × m × v²

→ The potential energy of a body is given by

  P.E = m g h

Answer 2

mass m= o.5kg

u=10m/s²

v= 20m/s²

Kinetic energy initial = 1/2mu² = 1/2×0.5×10²= 25J

Kinetic energy finally = 1/2mv²= 1/2×0.5×20²=100J

hence the change in Kinetic energy is

100J - 25J = 75J

work done = change in Kinetic energy

work done = 75J