A sledge of mass m slides down from point D onan icy hill of height h (as shown) and stops aftercovering a distance CB. The distance AB is equalto s. The co-efficient of friction between all thecontact surfaces is same.ADC Bh27. The co-efficient of friction between sledge and the icy surface is
Question
A sledge of mass m slides down from point D onan icy hill of height h (as shown) and stops aftercovering a distance CB. The distance AB is equalto s. The co-efficient of friction between all thecontact surfaces is same.ADC Bh27. The co-efficient of friction between sledge and the icy surface is
Solution
To determine the coefficient of friction between the sledge and the icy surface, we can use the information given in the problem.
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First, let's analyze the forces acting on the sledge as it slides down the icy hill. The main forces involved are the gravitational force (mg) and the frictional force (Ff).
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The gravitational force is acting vertically downwards and can be calculated using the mass of the sledge (m) and the acceleration due to gravity (g). So, the gravitational force is given by Fg = mg.
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The frictional force opposes the motion of the sledge and acts parallel to the surface of the icy hill. We can calculate the frictional force using the coefficient of friction (μ) and the normal force (N). The normal force is equal to the gravitational force acting on the sledge, so N = mg. Therefore, the frictional force is given by Ff = μN = μmg.
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Since the sledge stops after covering a distance CB, we can assume that the work done by the frictional force is equal to the change in gravitational potential energy. The work done by the frictional force is given by W = Ff * CB, and the change in gravitational potential energy is given by ΔPE = mgh.
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Equating the work done by the frictional force to the change in gravitational potential energy, we have μmg * CB = mgh.
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Simplifying the equation, we can cancel out the mass (m) on both sides, giving us μg * CB = gh.
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Finally, we can solve for the coefficient of friction (μ) by rearranging the equation: μ = (gh) / (g * CB).
Therefore, the coefficient of friction between the sledge and the icy surface is given by μ = (gh) / (g * CB).
Similar Questions
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The force of kinetic friction between two surfaces is independent of the area of contact between the surfaces.Group of answer choicesTrueFalse
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PERFECT NOW DO THE SAME THING BUT TELL ME IF EACH POINT HAS HIGH FRICTION ENERGY SOME FRICTION ENERGY AND NO FRICTION ENERGY PROVIDE EXPLIANTION ASWELL
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