A ball of mass 2 kg is thrown up with a velocity of 20 m s⁻¹.
Identify the sign of the work done by gravity on the ball during its upward motion and its downward motion.
During the upward motion, the force of gravity acts downwards while the displacement is upwards. Since force and displacement are in opposite directions, the work done by gravity is negative. During the downward motion, both the force of gravity and displacement are in the downward direction. Since they are in the same direction, the work done by gravity is positive.
If the ball reaches a height of 19.4 m, how much work was done by air resistance (assume g = 10 m s⁻²).
Step 1: Calculate Initial Kinetic Energy Using the expression for kinetic energy, K = 1/2 mv² K = 1/ kg × (20 m s⁻¹)² = 400 J.
Step 2: Calculate Final Potential Energy Using the expression for potential energy, PE = mgh PE = 2 kg × 10 m s⁻² × 19.4 m = 388 J.
Step 3: Calculate Work done by air resistance At the highest point, kinetic energy is zero and potential energy is maximum. The total energy at the bottom was 400 J, and at the top it is 388 J. The difference is the work done by air resistance. Work done by air resistance = Final Energy - Initial Energy = 388 J - 400 J = -12 J.
Explanation
For part (i), work done is determined by the angle between the force and displacement vectors. Gravity always acts downward. When the ball moves up, displacement is upward (opposite to force), so work is negative. When the ball moves down, displacement is downward (same direction as force), so work is positive. For part (ii), the principle of conservation of energy is applied, accounting for the work done by non-conservative forces (air resistance). The initial kinetic energy of the ball is transformed into potential energy at the maximum height and the work done against air resistance. Since the ball reaches a height of 19.4 m instead of the ideal 20 m (where all 400 J would convert to PE), the missing energy is the work done by air resistance.