A body of mass 5kg at rest is acted upon by two mutually perpendicular forces 6N and 8N simultaneously. Its kinetic energy after 10s is ___ in (J)

Explanation:

Step 1: Understanding the forces acting on the body

- The body has a mass of 5 kg.
- Two perpendicular forces of 6 N and 8 N act on the body.
- Since these forces are perpendicular, the motion in each direction can be analyzed independently.

Step 2: Calculating acceleration in each direction

Using Newton's second law, F = ma, the acceleration for each force is:

1. Force in the first direction (6 N):
   a1 = F1/m = 6/5 = 1.2 m/s2
2. Force in the second direction (8 N):
   a2 = F2/m = 8/5 = 1.6 m/s2

Step 3: Calculating velocity after 10 seconds

The body starts from rest, so the velocity in each direction after 10 seconds is:

1. Velocity in the first direction:
   v1 = a1 * t = 1.2 * 10 = 12 m/s
2. Velocity in the second direction:
   v2 = a2 * t = 1.6 * 10 = 16 m/s

Step 4: Calculating kinetic energy

The total kinetic energy is the sum of the kinetic energies in each direction. The formula for kinetic energy is:

K = 0.5 * m * v2

1. Kinetic energy in the first direction:
   K1 = 0.5 * 5 * (12)2 = 0.5 * 5 * 144 = 360 J
2. Kinetic energy in the second direction:
   K2 = 0.5 * 5 * (16)2 = 0.5 * 5 * 256 = 640 J

Step 5: Total kinetic energy

The total kinetic energy is the sum of K1 and K2:

K = K1 + K2 = 360 + 640 = 1000 J

Final Answer

The total kinetic energy of the body of mass 5 kg after 10 seconds is 1000 J.

Explanation of Motion

- The body of mass 5 kg experiences two accelerations, 1.2 m/s² and 1.6 m/s², due to the perpendicular forces.
- After 10 seconds, the velocities in the respective directions are 12 m/s and 16 m/s.
- The total kinetic energy is calculated by summing the kinetic energy contributions from each direction.

Using these calculations, we find that the kinetic energy of the body of mass 5 kg is 1000 J.