A chair of weight 145&nbsp;NN&nbsp;lies atop a horizontal floor; the floor is not frictionless. You push on the chair with a force of FF&nbsp;= 45.0 NN&nbsp;directed at an angle of 40.0 ∘&nbsp;∘&nbsp;below the horizontal and the chair slides along the floor.&nbsp;

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A chair of weight 145&amp;nbsp;NN&amp;nbsp;lies atop a horizontal floor; the floor is not frictionless. You push on the chair with a force of FF&amp;nbsp;= 45.0 NN&amp;nbsp;directed at an angle of 40.0 ∘&amp;nbsp;∘&amp;nbsp;below the horizontal and the chair slides along the floor.&amp;nbsp;

fudzisako · Accepted Answer

Let&#039;s denote:- Weight of the chair = W = 145 N- Applied force = F = 45.0 N- Angle of the applied force below the horizontal = θ = 40.0°The forces acting on the chair are:1. Weight of the chair, directed vertically downwards.2. Applied force, directed at an angle of 40.0° below the horizontal.3. Normal force exerted by the floor, perpendicular to the floor&#039;s surface.Since the chair is sliding along the floor, there must be a horizontal force component opposing the applied force. This horizontal force is due to the friction between the chair and the floor.The normal force and the vertical component of the applied force balance the weight of the chair:N−Wcos(θ)=0N=Wcos(θ)The horizontal component of the applied force and the friction force are equal in magnitude:Fsin(θ)=fwhere f is the magnitude of the friction force.Since the chair is sliding, the friction force can be calculated using the equation:f=μ·Nwhere μ is the coefficient of friction between the chair and the floor.Now, we need to find the coefficient of friction. We can rearrange the equation above and substitute the values:f=μ·Nf=μ·Wcos(θ)μ=fWcos(θ)μ=Fsin(θ)Wcos(θ)Substituting the given values, we have:μ=(45.0N)sin(40.0∘)(145N)cos(40.0∘)Evaluating this expression, we find:μ≈0.387Now that we have the coefficient of friction, we can determine the direction of motion. If the applied force is greater than the maximum static friction force (fmax=μ·N), the chair will move.In this case, the applied force F=45.0N is greater than the maximum static friction force, which is μ·N=μ·Wcos(θ).Therefore, the chair will move in the direction of the applied force.Hence, the chair will slide along the floor in the direction of the applied force, which is at an angle of 40.0° below the horizontal.

A chair of weight 145 NN lies

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