How to Calculate Work in Physics

The video begins with an introduction to the concept of work in physics, explaining it as a change in energy. The host, Physics Ninja, outlines the plan to cover three different cases of calculating work: constant forces, conservative forces, and work done as represented on a force versus position graph. The first example involves a block being dragged by a 50 Newton force at a 30-degree angle, with the goal of calculating the work done. The importance of understanding the angle between force and displacement is emphasized, and the work is calculated using the formula work = force * displacement * cos(θ), resulting in 520 joules.

This paragraph delves into calculating the work done by constant forces, using the example of a block on a surface. The host explains how to calculate the work done by the weight of the block (mg) and the normal force (n), both of which turn out to be zero due to the perpendicular angles to the displacement. The kinetic friction force is then considered, with its work calculated using the same formula as before but with the friction force and its angle of 180 degrees, resulting in -34 joules. The work energy theorem is introduced, stating that the net work done by all forces equals the change in kinetic energy of the object, and an example is worked out to find the final velocity of the block.

The host presents a scenario with a crate of mass m being dragged across the floor by different forces and displacements. The task is to rank the work done by the force F in four different cases from greatest to smallest. The work is calculated for each case using the formula work = force * displacement * cos(θ), and the results are compared. The case with the greatest force and displacement (case D) does the most work, while the case with the smallest force (case KC) does the least. The example illustrates the relationship between force magnitude, displacement, and the angle between them in determining the amount of work done.

The concept of conservative forces is introduced, with examples such as gravity, spring force, and electrical force. The host explains that conservative forces are associated with potential energy and that the work done by these forces depends only on the initial and final positions, not on the path taken. This path independence is a defining characteristic of conservative forces. The potential energy formulas for gravity (mg*h) and spring force (1/2*k*x^2) are provided, and it's noted that non-conservative forces, like friction, cannot be associated with potential energy and are path-dependent.

The calculation of work done by conservative forces is demonstrated using the formula work = -ΔU (final potential energy - initial potential energy). The host uses the example of a ball falling from a height to calculate the work done by gravity, resulting in a positive value of 185.2 joules. The same work is also calculated using the constant force equation, yielding the same result, reinforcing the equivalence of the two methods for conservative forces.

The host discusses the work done by gravity in two different scenarios: pushing a mass up a ramp and lifting it straight up. Despite the different paths, the work done by gravity is the same in both cases because gravity is a conservative force. The work is calculated using the formula work = -mg*y_final, resulting in -24.5 joules for each case. The negative sign indicates that the work is done against the direction of the force (uphill).

The host explains how to calculate the work done by a spring force, emphasizing that it's not constant and thus cannot be calculated using the work = FD*cos(θ) formula. Instead, the work is found by calculating the change in potential energy of the spring. An example is given where a 0.2 kg mass is stretched by 0.3 meters and released. The work done by the spring is calculated as 5.625 joules, which is positive because the force and displacement are in the same direction.

The host demonstrates how to calculate work from a force-position graph, explaining that the work done by a force is equal to the area under the curve. An example is provided where a force varies from 0 to 40 Newtons and then back to 0. The work is calculated by breaking the graph into simple shapes (triangles and a rectangle) and finding the area of each. The total work is found by summing the areas, resulting in 460 joules.

The final example shows how to calculate work from a graph where the force varies and includes a negative value. The host explains that the work done is represented by the area under the curve, regardless of whether the force is positive or negative. Two scenarios are considered: work done from x=0 to 7 meters and from x=0 to 14 meters. The work is calculated by finding the area under the curve for each segment, and it's shown that the total work over the entire displacement can be zero if positive and negative work cancel each other out.