An object of mass 5 kg falls from rest through a vertical distance of 20 m and gains a velocity of 10 m/s. The work done by the resistance of the air on the object will be

Explanation:

Given Data:

• Mass of the object, m = 5 kg
• Vertical distance fallen, h = 20 m
• Final velocity of the object, v = 10 m/s
• Initial velocity of the object, u = 0 m/s (since it falls from rest)
• Gravitational acceleration, g = 9.8 m/s²

Step 1: Calculate the potential energy lost by the object:

The potential energy (P.E.) lost by the object is given by:

P.E. = m × g × h

Substitute the given values:

P.E. = 5 × 9.8 × 20 = 980 J

Thus, the object loses 980 J of potential energy as it falls.

Step 2: Calculate the kinetic energy gained by the object:

The kinetic energy (K.E.) gained by the object is given by:

K.E. = 0.5 × m × v²

Substitute the given values:

K.E. = 0.5 × 5 × (10)² = 0.5 × 5 × 100 = 250 J

Thus, the object gains 250 J of kinetic energy during the fall.

Step 3: Calculate the work done by air resistance:

The work done by air resistance is equal to the difference between the potential energy lost and the kinetic energy gained:

Work done by air resistance = Potential energy lost - Kinetic energy gained

Work done by air resistance = 980 - 250 = 730 J

Since air resistance opposes the motion of the object, the work done by air resistance is negative:

Work done by air resistance = -730 J