Question Video: Calculating the Magnitude of a Force Acting on an Object in Equilibrium on a Rough Horizontal Plane | Nagwa Question Video: Calculating the Magnitude of a Force Acting on an Object in Equilibrium on a Rough Horizontal Plane | Nagwa

# Question Video: Calculating the Magnitude of a Force Acting on an Object in Equilibrium on a Rough Horizontal Plane Mathematics • Third Year of Secondary School

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A body weighing 25.5 N rests on a rough horizontal plane. A horizontal force acts on the body, causing it to be on the point of moving. Given that the coefficient of friction between the body and the plane is 3/17, determine the magnitude of the force.

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### Video Transcript

A body weighing 25.5 newtons rests on a rough horizontal plane. A horizontal force acts on the body, causing it to be on the point of moving. Given that the coefficient of friction between the body and the plane is three seventeenths, determine the magnitude of the force.

We can begin by sketching a diagram to model the situation. We know that any body resting on a horizontal plane will have a downward force equal to its weight. And this weight π will be equal to the mass of the body multiplied by the acceleration due to gravity. In this question, we are told the body weighs 25.5 newtons. So there will be a force acting vertically downwards equal to 25.5 newtons. Newtonβs third law tells us that there will be a normal reaction force acting in the opposite direction to this. Since the body is in equilibrium, we know that these two forces are equal. The normal reaction force π is equal to 25.5 newtons.

We are told that a horizontal force π acts on the body. And as the plane is rough, there will be a frictional force acting between the body and the plane. The body is on the point of moving, which means that the frictional force will be at its maximum. This is known as the limiting friction such that ππ is equal to π multiplied by π, where π is the coefficient of friction between the body and the plane. In this question, we are told this is equal to three seventeenths. The frictional force ππ is therefore equal to three seventeenths multiplied by 25.5, which is equal to 4.5. The maximum frictional force is equal to 4.5 newtons.

Since the body is on the point of moving and is still in equilibrium, the horizontal forces must also be equal to one another. The applied force π must be equal to the frictional force ππ. We can therefore conclude that the magnitude of the horizontal force acting on the body is 4.5 newtons.

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