Summary Tradisional | Work: Weight

Contextualization

In Physics, work is closely connected to applying a force that results in displacement. Unlike how we commonly use the term in our daily lives, where it refers to any activity we do, in Physics, work specifically measures the energy transferred by the force. For instance, when we push a box across the floor, we are performing work because we are applying a force that moves the box in the direction we push it.

The weight force, which is the force that pulls objects towards the Earth's centre due to gravity, also does work. When we lift something off the ground to a certain height, we can calculate the work done by the weight force using the formula τ = mgh, where m signifies the object's mass, g represents the acceleration due to gravity (approximately 9.81 m/s² on Earth’s surface), and h denotes the height change. This concept is crucial for understanding various physical phenomena and their applications, such as how elevators operate and the free fall of objects.

To Remember!

Concept of Work in Physics

In Physics, the concept of work relates to a force applied that leads to displacement. Work is essentially the energy transferred by this force throughout the displacement. The general formula for calculating work is τ = F * d * cos(θ), where F indicates the force, d is the displacement, and θ denotes the angle between the force and displacement. It's important to note that work is accomplished only when there's a displacement occurring in the same direction as the applied force.

Work can be either positive or negative. It is considered positive when the force and displacement align, like pushing something forward. Conversely, work is negative when the force acts against the displacement, such as applying brakes in a vehicle. If the force is perpendicular to the displacement, as when an object moves in a circle under centripetal force, the work done is zero.

In day-to-day language, while we think of work as any activity, in Physics, it refers specifically to the energy transfer caused by a force. For example, when a box is pushed along the floor, work is being done because of the applied force leading to its displacement. This concept is vital for understanding energy transfer and transformation in different physical systems.

• Work is the energy transferred by a force across a displacement.

• The general formula is τ = F * d * cos(θ).

• Work can be positive, negative, or zero, based on the direction of the force relative to displacement.

Work of the Weight Force

The weight force is a conservative force that operates on objects because of gravity. The work done by this weight force can be calculated with the formula τ = mgh, where m represents the object's mass, g is the gravitational acceleration (approximately 9.81 m/s² at Earth's surface), and h indicates the vertical height change. This formula holds when the weight force is the sole force acting and the object is moving upward or downward vertically.

When we lift something from the floor to a height, we are exerting work against the weight force. Here, the work done by the weight force turns out to be negative, as gravity pulls in the opposite direction of the lift. On the flip side, if an object is dropped, the work done by the weight force is positive because the gravitational force and the object’s descent align.

Comprehending the work of the weight force is vital for grasping numerous natural and technological occurrences. For instance, in operating elevators, the physics behind free-falling objects, and many other systems where gravity is a key player, the concept of work done by the weight force plays an essential role.

• The weight force is a conservative force due to gravity.

• The formula for calculating the work of the weight force is τ = mgh.

• Work may be positive or negative, depending on how the displacement interacts with the weight force.

Practical Examples

To illustrate the concept of the work done by the weight force, let’s look at some practical examples. Imagine lifting a 1 kg book onto a 1-meter high table. Here, the mass of the book (m) is 1 kg, the gravitational acceleration (g) is 9.81 m/s², and h is 1 meter. Using the formula τ = mgh, we find τ = 1 kg * 9.81 m/s² * 1 m = 9.81 Joules. Thus, the work done against the weight force is 9.81 J.

Another scenario is dropping a 2 kg object from a height of 3 meters. In this case, the mass (m) is 2 kg, g is 9.81 m/s², and h equals 3 meters. By using the formula τ = mgh, we arrive at τ = 2 kg * 9.81 m/s² * 3 m = 58.86 Joules. The work performed by the weight force is 58.86 J and is positive because the direction of movement aligns with the force.

These instances show us how to utilise the formula τ = mgh for calculating the work of the weight force in different situations. Regular practice with varied examples enhances the understanding of the concept and its relevance to real-life interactions.

• Case of lifting a 1 kg book from the ground to a 1-meter high table.

• Case of dropping a 2 kg object from a height of 3 meters.

• Working through different examples solidifies the grasp of the concept.

Guided Problem Solving

To apply the formula for the work of the weight force across various scenarios, solving problems step by step is highly productive. Let’s consider some common examples. Suppose we lift an object weighing 5 kg to a height of 2 meters. Using the formula τ = mgh where m = 5 kg, g = 9.81 m/s², and h = 2 meters, we find τ = 5 kg * 9.81 m/s² * 2 m = 98.1 Joules. Hence, the work done against the weight force is 98.1 J.

Another example involves working out the weight force’s contribution when lowering a 10 kg item from a height of 3 meters. Here, m = 10 kg, g = 9.81 m/s², and h = 3 meters. By substituting the values, we see τ = 10 kg * 9.81 m/s² * 3 m = 294.3 Joules. This indicates that the work done is 294.3 J, considering the downward movement represents negative displacement.

Lastly, take a 7 kg object hurled upwards, reaching a maximum height of 4 meters. In this case, m = 7 kg, g = 9.81 m/s², and h = 4 meters. We calculate τ = 7 kg * 9.81 m/s² * 4 m = 274.68 Joules, yielding -274.68 J (negative work) as the weight force acts in opposition to the upward movement.

• Example of a 5 kg object lifted to a height of 2 meters.

• Example of a 10 kg object lowered from a height of 3 meters.

• Example of a 7 kg object thrown upwards, hitting a height of 4 meters.

Key Terms

• Work: Measure of the energy transferred by a force over a displacement.

• Weight Force: The force through which gravity pulls an object towards Earth’s center.

• Formula τ = mgh: Formula used for computing the work of the weight force, where m is mass, g is gravitational acceleration, and h is the height change.

• Positive Work: Occurs when the force and displacement are in the same direction.

• Negative Work: Occurs when the force and displacement are in opposite directions.

Important Conclusions

In this lesson, we delved into the work concept in Physics, with a particular emphasis on the weight force. We discovered that work signifies the energy transferred by a force across displacement and that the formula for work concerning the weight force is τ = mgh. We examined how work can be categorized as positive or negative, based on the displacement relative to the gravitational force.

Through hands-on examples and guided problem-solving, we learnt how to implement the formula τ = mgh to ascertain the work attributed to the weight force in distinct scenarios, such as lifting and dropping objects. These examples pave the way for linking theoretical knowledge to practical applications, evident in everyday experiences like the functioning of elevators and the free fall of objects.

Grasping the work of the weight force is fundamental to Physics, providing clarity on both natural and technological occurrences. This information is applicable across many fields, from engineering to meteorology, underscoring the vital role of Physics in our everyday life.

Study Tips

• Revisit the practical cases discussed in the lesson and attempt additional problems to solidify knowledge about the work of the weight force.

• Explore online Physics simulators to visualize the workings of the weight force in various scenarios and changes in height.

• Form study groups to collaboratively tackle problems, clearing doubts and enhancing group learning.