Question Video: Finding the Force Exerted on a Pulley Connecting a Body on a Smooth Surface to a Vertically Hanging Body | Nagwa Question Video: Finding the Force Exerted on a Pulley Connecting a Body on a Smooth Surface to a Vertically Hanging Body | Nagwa

Question Video: Finding the Force Exerted on a Pulley Connecting a Body on a Smooth Surface to a Vertically Hanging Body Mathematics • Third Year of Secondary School

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A body is placed on a smooth horizontal table. It is connected, by a light inextensible string over a smooth pulley fixed at the edge of the table, to another body hanging freely vertically below the pulley. If the tension in the string was 1.04 N, find the force exerted on the pulley.

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Video Transcript

A body is placed on a smooth horizontal table. It is connected, by a light inextensible string over a smooth fixed pulley at the edge of the table, to another body hanging freely vertically below the pulley. If the tension in the string was 1.04 newtons, find the force exerted on the pulley.

We will begin by sketching a diagram of the situation. As our string is light and inextensible, we know that the tensions moving towards the pulley will be equal in value. In this question, these are equal to 1.04 newtons. As the table and pulley are both smooth, there will be no frictional force. The resultant force on the pulley will be in the direction shown. As the two tension forces meet at 90 degrees, each of these will be 45 degrees from the resultant force.

Resolving in this direction, we see that the resultant force is equal to 𝑇 cos 45 degrees plus 𝑇 cos 45 degrees. This is equal to two 𝑇 multiplied by cos 45 degrees. And as 𝑇 is equal to 1.04, we need to multiply two, 1.04, and cos 45 degrees. We know that cos of 45 degrees is equal to root two over two, and multiplying this by 2.08 gives us 26 root two over 25. The force exerted on the pulley is therefore equal to 26 root two over 25 newtons.

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