- For part C.1: The work done by the new force is less than the work done by the original force. Work is defined as W = F·d·cosθ, where θ is the angle between the force vector and the displacement vector. In the original case, θ = 0°, so cosθ = 1 and work is maximized. In the new case, θ > 0°, so cosθ < 1, reducing the work done for the same magnitude of force and displacement.
- For part C.2: The arrow representing the direction of the force must be perpendicular to the displacement (i.e., pointing straight up or straight down). Since work is zero when the force is perpendicular to displacement (cos90° = 0), the force vector must be vertical while displacement is horizontal.
- For part D:
- The hand’s pushing force does positive work because it acts in the direction of displacement.
- Gravity does zero work because it acts vertically downward while displacement is horizontal (perpendicular).
- The normal force from the table does zero work for the same reason — it acts vertically upward, perpendicular to horizontal displacement.
- Friction (if present) would do negative work if it opposes motion, but since no friction is mentioned and motion occurs, we assume a frictionless surface; thus, only the hand’s force does work.
- Net work is positive because the block moves in the direction of the applied force, indicating energy is transferred to the block.
- Net work is equal to the work done by the net force on the block because, by definition, net work is the sum of work done by all individual forces, which equals the work done by the vector sum of those forces (the net force).
- For part E:
- If net work is positive, the object’s speed increases (kinetic energy increases).
- If net work is negative, the object’s speed decreases (kinetic energy decreases).
- If net work is zero, the object’s speed remains constant (kinetic energy unchanged).
- These results are consistent with the work-energy theorem (W_net = ΔK = K_final - K_initial), which states that the net work done on an object equals its change in kinetic energy. Positive net work increases kinetic energy (and thus speed), negative net work decreases it, and zero net work means no change in kinetic energy or speed.
Parent Tip: Review the logic above to help your child master the concept of work energy theorem worksheet.
