Final answer:
To determine the work done by tension force, calculate the product of the force component in the direction of the displacement and the magnitude of the displacement along that direction. If an object is lifted at a constant velocity, work is simply the tension force times height.
Step-by-step explanation:
To find the work done by tension force, we must first understand what tension is and how it functions in physics. Tension is a pulling force transmitted along the length of a wire, rope, cable, or any object that can be stretched. It is tangential to the wire and has the units of force (Newtons, N).
When a force is applied to a mass by a tension in a rope, and the mass moves a certain distance, we can calculate the work done. Work is defined as the product of the force component in the direction of motion and the displacement. The formula for work (W) is given by:
W = Fd cosθ
Where F is the tension force, ‘d’ is the displacement, and θ is the angle between the force applied and the direction of displacement. If the tension is in the same direction as displacement, the cosine factor is 1 because cos 0° = 1, and the work done is simply F times ‘d’.
Consider a case where you have a rope subjected to tension T due to a force F applied at its ends. This rope passes over a pulley and is used to lift a mass m. Assuming that there is no friction and the pulley is massless, the tension in the rope would be equal to the weight of the mass being lifted, provided the mass moves upwards with a constant velocity (thus acceleration is zero). By Newton's second law, Fnet = 0, therefore T = mg where ‘g’ is the acceleration due to gravity.
To calculate the work done by the tension force while lifting the object, if T is the magnitude of the tension and the object is lifted to height ‘h’, the work done by tension, W, is:
W = Th
If, on the other hand, the object is being accelerated upwards, not only must the tension overcome the gravitational force but also provide the extra force necessary for acceleration. Therefore, T = mg + ma where ‘a’ is the acceleration. In such a case, to find the work done by tension while lifting the object through height ‘h’, the tension force is multiplied by the vertical displacement. The work done is then:
W = (mg + ma)h
These principles are widely applied in engineering, physics, and daily practicalities where tension forces and mechanics are at play.