Summary Tradisional | Work: Weight

Contextualization

In Physics, the concept of work is fundamentally tied to the application of a force that results in displacement. This is different from how we commonly use 'work,' which refers to any activity undertaken. In physics terms, work quantifies the energy transferred by a force. For instance, when we push a box across the floor, we're performing work since we apply a force that moves the box in the direction of that force.

The weight force, the pull exerted by gravity on an object towards the centre of the Earth, also performs 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 represents the object's mass, g is the acceleration due to gravity (approximately 9.81 m/s² at Earth's surface), and h is the change in height. This concept is essential for comprehending various physical phenomena and their real-world applications, such as how elevators function and the free-falling motion of objects.

To Remember!

Concept of Work in Physics

In Physics, work refers to the energy transitioned due to the application of a force that causes a displacement. The general formula for calculating work is τ = F * d * cos(θ), where F is the force applied, d is the displacement, and θ is the angle between the force and the path of displacement. It’s crucial to note that work occurs only when there is a displacement in the direction of the force.

Work can be classified as positive or negative. It is positive when the force and displacement align, such as pushing a cart forward. Conversely, work is negative when the force and displacement are opposite, for instance when you brake a vehicle. When the force is perpendicular to the displacement, like an object moving in a circle under centripetal force, the work done amounts to zero.

Unlike its everyday meaning, which refers broadly to any activity, in Physics, work serves as a distinct measure of energy transferred by a force. In practice, when we push a box on the floor, this exemplifies work, since we are applying a force that causes a displacement in the direction of that force. This principle is key to grasping how energy shifts and transforms across various physical systems.

• Work is the energy transferred by a force over a distance.

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

• Work can be positive, negative, or zero, based on the relationship between force and displacement.

Work of the Weight Force

The weight force is a conservative force acting on objects as a result of gravity. The work performed by the weight force is expressed with the formula τ = mgh, in which m represents the object's mass, g is the acceleration from gravity (about 9.81 m/s² at Earth’s surface), and h is the change in height. This formula applies when the weight force is the sole force at work and the object moves vertically.

When we lift something from the ground to a height, we're doing work against the weight force. Therefore, the work done by the weight force is considered negative, as gravity acts opposite to the direction we're moving. However, if we drop an object, the work done by the weight force is positive because both gravity and the movement are in the same direction.

Comprehending the work of the weight force is essential for understanding various phenomena in nature and technology. For example, the calculations around the work by the weight force are critical for the operation of elevators, the free fall of objects, and many other systems that rely heavily on gravity.

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

• The work of the weight force is calculated with τ = mgh.

• The nature of work can be positive or negative, depending on the relationship between displacement and the weight force.

Practical Examples

To clarify the work of the weight force, let’s look at some practical examples. Consider lifting a 1 kg book from the floor to a table 1 meter high. In this case, the mass (m) is 1 kg, gravity’s acceleration (g) is 9.81 m/s², and the height (h) is 1 meter. When we apply 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.

In another scenario, dropping a 2 kg object from a height of 3 meters can be considered. Here, m is 2 kg, g is still 9.81 m/s², and h is 3 meters. Substituting into our formula gives τ = 2 kg * 9.81 m/s² * 3 m = 58.86 Joules. The work done by the weight force in this case is 58.86 J, which is positive as the direction of movement aligns with the gravitational force.

These examples illustrate how to use the τ = mgh formula for calculating the work of the weight force in various contexts. Practicing with different scenarios reinforces understanding of the concept and its real-world application.

• Example of lifting a 1 kg book to a 1-meter high table.

• Example of a 2 kg object being dropped from a height of 3 meters.

• Working through diverse examples solidifies comprehension of the concept.

Guided Problem Solving

To put the formula for the work of the weight force into practice across various situations, it helps to solve problems step by step. For instance, if we lift a 5 kg object to a height of 2 meters, we use τ = mgh, where m = 5 kg, g = 9.81 m/s², and h = 2 meters. Plugging in the numbers, we find τ = 5 kg * 9.81 m/s² * 2 m = 98.1 Joules. Thus, the work against the weight force is 98.1 J.

As another example, let’s calculate the work done by the weight force when lowering a 10 kg object from 3 meters high. This time, m = 10 kg, g = 9.81 m/s², and h = 3 meters. Substituting in gives us τ = 10 kg * 9.81 m/s² * 3 m = 294.3 Joules. In this case, the work done, where the displacement is downward, is 294.3 J.

Lastly, think of a 7 kg object thrown upwards, reaching a peak height of 4 meters. Here, m = 7 kg, g = 9.81 m/s², and h = 4 meters. Using the formula results in τ = 7 kg * 9.81 m/s² * 4 m = 274.68 Joules. Note that the work done during the upward movement is -274.68 J (negative work) since the weight force opposes the upward direction.

• 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 to a height of 4 meters.

Key Terms

• Work: A measure of the energy transferred by a force through displacement.

• Weight Force: The gravitational pull on an object towards the Earth's center.

• Formula τ = mgh: Formula for calculating the work of the weight force where m is the mass, g is the acceleration due to gravity, and h is the height change.

• Positive Work: When the force and displacement are oriented in the same direction.

• Negative Work: When the force and displacement are oriented in opposing directions.

Important Conclusions

In this lesson, we covered the concept of work in Physics, with a distinct focus on the weight force. We learned that work quantifies the energy transferred by a force over displacement, and the formula for the work of the weight force is τ = mgh. We discussed how the nature of work can be positive or negative depending on the direction of displacement related to gravitational force.

Through practical examples and guided problem-solving, we learned to apply the formula τ = mgh for calculating the work done by the weight force in various circumstances like lifting an object or letting it drop. These scenarios bridge theoretical concepts with real-life applications, for instance, how elevators operate and the free fall of objects.

Grasping the work performed by the weight force is key to understanding Physics, enhancing our comprehension of natural and technological phenomena. This knowledge finds relevance across numerous fields, from engineering to meteorology, underscoring the vital role of Physics in our daily lives.

Study Tips

• Revisit the practical examples discussed in class and try solving additional problems to solidify your grasp of the work of the weight force.

• Leverage online Physics simulators to visualize how the weight force performs work across different heights and settings.

• Form study groups to collaborate on problem-solving, which can clarify uncertainties and bolster team learning.