G We saw in class that in a pendulum the string does no work. We also saw that the normal force does no work on an object sliding down a ramp. (a) Explain why the tension in the string of a pendulum does no work. (b) Explain why the normal force does no work on an object sliding down a ramp. (c) Give an example of a situation where tension does do work on an object. (d) Give an example of a situation where friction does positive work on something.

a) θ=90º, b) θ=90º, c) θ=0º W =F x, d) θ=180º W = -fr x

Explanation:

The job is defined by

       W = F. dx

Where the point is the dot product

      W = F dx cos θ

Let's apply this equation to our case

a) the attention is perpendicular to the arc of the displacement, and the displacement is parallel to the arc, so the angle between the tension and the displacement is 90º so the cosine is zero

        W = 0

b) The normal is the reaction to the weight of the body, so it is perpendicular to the surface and the displacement is parallel to the surface, the angle between these two is 90º

      W = 0

c) when we pull a body with a rope the tension of the rope does work on the body

         W = T x

d) When we pull a body on a rough surface, the friction force creates a job because it is the angle between friction and the 180º displacement

         W = - fr x

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