Certainly! Here are seven WAEC/WASSCE-style questions on Work, Energy, and Power, along with their solutions:
Question 1:
A force of 10 N is applied to move a box 5 m along a surface. Calculate the work done against friction if the entire movement occurs along the horizontal surface.
Solution: Work done (W) is calculated using the formula: \[ W = F \cdot d \cdot \cos(\theta) \] where:
- \( F = 10 , \text{N} \) (force applied)
- \( d = 5 , \text{m} \) (distance moved)
- \( \theta = 0^\circ \) (because the force is in the direction of motion)
Since \( \cos(0^\circ) = 1 \): \[ W = 10 , \text{N} \cdot 5 , \text{m} \cdot 1 = 50 , \text{J} \]
Question 2:
An object of mass 2 kg is lifted to a height of 4 m. Calculate the gravitational potential energy gained by the object. (Take \( g = 9.8 , \text{m/s}^2 \))
Solution: Gravitational potential energy (PE) is calculated using the formula: \[ PE = mgh \] where:
- \( m = 2 , \text{kg} \)
- \( g = 9.8 , \text{m/s}^2 \)
- \( h = 4 , \text{m} \)
Substituting the values: \[ PE = 2 , \text{kg} \cdot 9.8 , \text{m/s}^2 \cdot 4 , \text{m} = 78.4 , \text{J} \]
Question 3:
A car of mass 1000 kg is moving at a speed of 20 m/s. Calculate its kinetic energy.
Solution: Kinetic energy (KE) is calculated using the formula: \[ KE = \frac{1}{2} mv^2 \] where:
- \( m = 1000 , \text{kg} \)
- \( v = 20 , \text{m/s} \)
Substituting the values: \[ KE = \frac{1}{2} \cdot 1000 , \text{kg} \cdot (20 , \text{m/s})^2 = 200,000 , \text{J} \]
Question 4:
A machine does 3000 J of work in 60 seconds. What is the power output of the machine?
Solution: Power (P) is calculated using the formula: \[ P = \frac{W}{t} \] where:
- \( W = 3000 , \text{J} \)
- \( t = 60 , \text{s} \)
Substituting the values: \[ P = \frac{3000 , \text{J}}{60 , \text{s}} = 50 , \text{W} \]
Question 5:
A 5 kg block is raised vertically from rest through a height of 3 m. Calculate the work done on the block against gravity.
Solution: Using the formula for work done against gravity: \[ W = mgh \] where:
- \( m = 5 , \text{kg} \)
- \( g = 9.8 , \text{m/s}^2 \)
- \( h = 3 , \text{m} \)
Substituting the values: \[ W = 5 , \text{kg} \cdot 9.8 , \text{m/s}^2 \cdot 3 , \text{m} = 147 , \text{J} \]
Question 6:
A bicycle with a mass of 15 kg accelerates from rest to a speed of 10 m/s. Calculate the work done by the bicycle to achieve this speed.
Solution: First, calculate the kinetic energy (KE): \[ KE = \frac{1}{2} mv^2 \] where:
- \( m = 15 , \text{kg} \)
- \( v = 10 , \text{m/s} \)
Substituting the values: \[ KE = \frac{1}{2} \cdot 15 , \text{kg} \cdot (10 , \text{m/s})^2 = 750 , \text{J} \]
The work done (W) is equal to the change in kinetic energy: \[ W = 750 , \text{J} \]
Question 7:
If a car consumes 600,000 J of energy in 2 minutes, what is the average power output of the car in watts?
Solution: Power (P) is calculated using the formula: \[ P = \frac{W}{t} \] where:
- \( W = 600,000 , \text{J} \)
- \( t = 2 , \text{minutes} = 2 \cdot 60 = 120 , \text{s} \)
Substituting the values: \[ P = \frac{600,000 , \text{J}}{120 , \text{s}} = 5000 , \text{W} \]
This completes your set of WAEC/WASSCE-style questions on Work, Energy, and Power with solutions!
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