A man picks up a bag of weight of 15 kg from the ground and puts it on his head 1.5 m above the ground. What is the work done by him on the bag? ( g = 10 m/s 2 )
225 J
Understanding the Physics Problem: Work Done
The problem asks us to calculate the work done by a man when he lifts a bag from the ground and places it on his head. In physics, work is done when a force is applied to an object, and the object moves in the direction of the force. When lifting an object against gravity, the force applied is typically equal to the weight of the object, and the distance is the vertical height it is lifted.
Analyzing the Given Information
We are provided with the following values:
- Mass of the bag (\(m\)) = 15 kg
- Height the bag is lifted (\(h\)) = 1.5 m
- Acceleration due to gravity (\(g\)) = 10 m/s\(^2\)
We need to find the work done by the man on the bag.
Calculating the Force Applied
To lift the bag, the man must exert an upward force at least equal to the weight of the bag to overcome the force of gravity. The weight of an object is calculated using the formula:
\[ \text{Weight} = \text{mass} \times \text{acceleration due to gravity} \] \[ F = m \times g \]Substituting the given values:
\[ F = 15 \, \text{kg} \times 10 \, \text{m/s}^2 \] \[ F = 150 \, \text{N} \]The force applied by the man to lift the bag is 150 Newtons.
Calculating the Work Done by the Man
Work done (\(W\)) is defined as the product of the force applied and the distance moved in the direction of the force. In this case, the force is applied upwards, and the bag is moved upwards.
The formula for work done is:
\[ W = \text{Force} \times \text{Distance} \] \[ W = F \times h \]Now, substituting the calculated force and the given height:
\[ W = 150 \, \text{N} \times 1.5 \, \text{m} \] \[ W = 225 \, \text{J} \]The work done by the man on the bag is 225 Joules.
The unit of work is the Joule (J), which is equivalent to a Newton-meter (Nm).
Summary of the Work Done Calculation
The work done by the man to lift the 15 kg bag to a height of 1.5 m against gravity (10 m/s²) is 225 Joules.
Revision Table: Important Physics Concepts
| Concept | Definition/Formula | Standard Unit |
|---|---|---|
| Work Done (\(W\)) | Force \(\times\) Distance moved in direction of force (\(W = F \times d\)) | Joules (J) |
| Force (F) | Mass \(\times\) Acceleration (\(F=ma\)). Weight is Force due to gravity (\(F=mg\)) | Newtons (N) |
| Weight | The force exerted by gravity on an object (\(W_{gravity} = mg\)) | Newtons (N) |
| Mass (\(m\)) | A measure of the amount of matter in an object | Kilograms (kg) |
| Distance (\(d\) or \(h\)) | Length of the path travelled | Meters (m) |
| Acceleration due to gravity (\(g\)) | Acceleration of a freely falling body due to gravity | m/s\(^2\) |
Additional Information: Work, Energy, and Gravity
When work is done against a conservative force like gravity, the work done results in a change in potential energy. The work done by the man in lifting the bag increases the gravitational potential energy (\(PE\)) of the bag.
The gravitational potential energy gained is given by the formula:
\[ \Delta PE = mgh \]Let's calculate the potential energy gained using the given values:
\[ \Delta PE = 15 \, \text{kg} \times 10 \, \text{m/s}^2 \times 1.5 \, \text{m} \] \[ \Delta PE = 225 \, \text{J} \]Notice that the work done by the man (225 J) is exactly equal to the gravitational potential energy gained by the bag (225 J). This demonstrates the relationship between work done against gravity and the change in potential energy.
Important Questions from Potential Energy
Which one of the following is not a conservative force ?
Which of the following is an example of gravitational potential energy?
What type of energy conversion takes place during the thunder of clouds?
The potential difference is 40V. Find the work done to transmit a charge of 0.5C?
Which of the following terms is used for stored energy that depends upon the relative position of various parts of a system?
