Question
Pls provide me with seven WAEC/WASSCE questions on Work, Energy and power WITH THEIR SOLUTIONS
Answers
GPT-4o mini
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!
### 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!