Energy and Work - Multiple Choice Test Notes

Conceptual Questions

  • Work (SI unit): Joule (J)
  • Work Definition:
    • Work is defined as Force × distance × cosine of the angle between force and displacement. Mathematically, this is represented as W=F⋅d⋅cos⁡(θ)W = F \cdot d \cdot \cos(\theta)
  • Situations where work is done:
    • Work is done when a force causes an object to move. For example, a person pushes a box, and it moves.
  • Work done when the angle between force and displacement is 90°:
    • If the angle between the force and displacement is 90°, the work done is zero because cos⁡(90∘)=0\cos(90^\circ) = 0.
  • Energy associated with motion:
    • Kinetic energy is associated with motion.
  • Gravitational potential energy depends on:
    • Height and mass. The formula is PE=mghPE = mgh, where mm is mass, gg is the acceleration due to gravity, and hh is height.
  • Law of Conservation of Energy:
    • Energy cannot be created or destroyed; it can only be transformed from one form to another.
  • Power Definition:
    • Power is defined as work per unit time. Mathematically, P=WtP = \frac{W}{t}
  • Unit to measure power:
    • Watt (W)
  • Efficient machine:
    • A machine is efficient if it converts more input energy into useful output.

Calculation-Based Questions

  • Question 11:
    • Given: Force = 10 N, distance = 5 m.
    • Work done = Force × distance = 10 N×5 m=50 J10 \text{ N} \times 5 \text{ m} = 50 \text{ J}.
  • Question 12:
    • Given: mass = 2 kg, height = 3 m, g=9.8 m/s2g = 9.8 \text{ m/s}^2
    • Potential energy = mgh=2 kg×9.8 m/s2×3 m=58.8 Jmgh = 2 \text{ kg} \times 9.8 \text{ m/s}^2 \times 3 \text{ m} = 58.8 \text{ J}.
  • Question 13:
    • Given: mass = 4 kg, velocity = 3 m/s.
    • Kinetic energy = 12mv2=12×4 kg×(3 m/s)2=18 J\frac{1}{2}mv^2 = \frac{1}{2} \times 4 \text{ kg} \times (3 \text{ m/s})^2 = 18 \text{ J}.
  • Question 14:
    • Given: Power = 100 W, time = 2 minutes = 120 seconds.
    • Energy used = Power × time = 100 W×120 s=12,000 J100 \text{ W} \times 120 \text{ s} = 12,000 \text{ J}.
  • Question 15:
    • Given: Force = 15 N, angle = 60°, distance = 4 m.
    • Work done = Fdcos⁡(θ)=15 N×4 m×cos⁡(60∘)=15 N×4 m×0.5=30 JFd \cos(\theta) = 15 \text{ N} \times 4 \text{ m} \times \cos(60^\circ) = 15 \text{ N} \times 4 \text{ m} \times 0.5 = 30 \text{ J}.
  • Question 16:
    • Given: Work = 20,000 J, time = 10 seconds.
    • Power = Work / time = 20,000 J10 s=2,000 W\frac{20,000 \text{ J}}{10 \text{ s}} = 2,000 \text{ W}.
  • Question 17:
    • Given: height = 10 m, g=9.8 m/s2g = 9.8 \text{ m/s}^2.
    • Speed = 2gh=2×9.8 m/s2×10 m=196=14 m/s\sqrt{2gh} = \sqrt{2 \times 9.8 \text{ m/s}^2 \times 10 \text{ m}} = \sqrt{196} = 14 \text{ m/s}.
  • Question 18:
    • When a person pushes against a wall with 100 N for 10 seconds, but the wall doesn’t move, the work done is 0 J because there is no displacement.
  • Question 19:
    • Given: mass = 60 kg, height = 20 m.
    • Potential energy = mgh=60 kg×9.8 m/s2×20 m=11,760 Jmgh = 60 \text{ kg} \times 9.8 \text{ m/s}^2 \times 20 \text{ m} = 11,760 \text{ J}. (Closest answer is 12,000 J)
  • Question 20:
    • Given: mass = 2 kg, velocity = 10 m/s.
    • Kinetic energy = 12mv2=12×2 kg×(10 m/s)2=100 J\frac{1}{2}mv^2 = \frac{1}{2} \times 2 \text{ kg} \times (10 \text{ m/s})^2 = 100 \text{ J}.

Mixed and Application Questions

  • Kinetic Energy increase:
    • Increasing its speed increases an object's kinetic energy.
  • Machine Efficiency:
    • Given: Efficiency = 75%, Input energy = 200 J.
    • Useful output = Efficiency × Input = 0.75×200 J=150 J0.75 \times 200 \text{ J} = 150 \text{ J}.
  • Work (Scalar Quantity):
    • Work is a scalar quantity because it has magnitude only.
  • Energy Transformation (Rubbing Hands):
    • Mechanical to thermal energy transformation occurs when you rub your hands together.
  • Work (Holding Object at Constant Velocity):
    • No work is done when a person walks holding a heavy object at constant velocity on a flat surface because the force is perpendicular to the displacement.
  • Kinetic Energy Doubles:
    • If the kinetic energy of an object doubles, its speed increases by 2\sqrt{2}.
  • Simple Machine (Wasted Work):
    • Given: Efficiency = 40%, Input = 100 J.
    • Wasted work = Input × (1 - Efficiency) = 100 J×(1−0.40)=60 J100 \text{ J} \times (1 - 0.40) = 60 \text{ J}.
  • Negative Work:
    • Pushing against a moving object to slow it down shows negative work.
  • Power Output:
    • Doing 50 J of work in 5 seconds results in the most power output, as P=50 J5 s=10 WP = \frac{50 \text{ J}}{5 \text{ s}} = 10 \text{ W}.
  • Force and Work Relationship:
    • The graph that best represents the relationship between force and work (when displacement is constant) is a straight line increasing.