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Lesson Worksheet: The Equilibrium of a Body on a Rough Inclined Plane Mathematics

In this worksheet, we will practice solving problems on the equilibrium of a body on a rough inclined plane.

Q1:

A body weighing 195 N is on a rough plane that is inclined at an angle of 45 to the horizontal. If the coefficient of friction between the body and the plane is 33, which of the following is true about the body?

  • AThe body is in a stable state of equilibrium.
  • BThe body is sliding down the plane.
  • CThe body is on the point of sliding down the plane.

Q2:

The figure shows a body of weight 46 N resting on a rough inclined plane. Given that the body is on the point of sliding down the plane and that the coefficient of static friction is 3, find the magnitude of the limiting friction.

  • A46 N
  • B233 N
  • C23 N
  • D463 N

Q3:

A body weighing 60 N rests on a rough plane inclined to the horizontal at an angle whose sine is 35. The body is pulled upward by a force of 63 N acting parallel to the line of the greatest slope. Given that the body is on the point of moving up the plane, find the coefficient of friction between the body and the plane.

  • A34
  • B716
  • C916
  • D2120
  • E920

Q4:

The figure shows a body resting on a rough inclined plane where the coefficient of static friction between the body and the plane 𝜇=0.487. Given that the body is on the point of sliding down the plane, find the angle of inclination 𝜃 rounding your answer to the nearest minute if necessary.

  • A642
  • B299
  • C2558
  • D6051

Q5:

The figure shows a body on a rough inclined plane. Given that it is on the point of sliding down the plane, find the measure of the angle of static friction between the body and the plane rounding your answer to the nearest minute if necessary.

  • A3737
  • B3514
  • C7310
  • D1650

Q6:

A body of weight 438 N rests on a rough plane inclined at an angle of 30 to the horizontal. The coefficient of friction between the body and the plane is 32. A force acts on the body such that its line of action is parallel to the line of greatest slope. As a result, the body is on the point of moving up the plane. Determine the magnitude of the force.

Q7:

A body weighing 200 N rests on a rough plane inclined at an angle of 30 to the horizontal. The body is pulled upward by a string making an angle of 30 to the line of greatest slope of the plane. When the tension in the string is 803 N, the body is on the point of moving up the plane. Find the coefficient of friction between the body and the plane.

  • A39
  • B33
  • C315
  • D11321

Q8:

A body weighing 56 N rests on a rough plane inclined at an angle of 30 to the horizontal. The coefficient of friction between the body and the plane is 36. The body is pulled upward by a string making an angle of 30 to the line of greatest slope of the plane. Determine the minimum tension in the string required to cause the body to be on the point of moving up the plane.

  • A243 N
  • B83 N
  • C5635 N
  • D56 N
  • E283 N

Q9:

When a body of weight 262.5 N was resting on a rough plane inclined to the horizontal at an angle whose tangent is 34, it was on the point of moving. The same body was later placed on a horizontal surface of the same roughness. A force 𝐹 acted on the body pulling upward at an angle of 𝜃 to the horizontal where sin𝜃=35. Given that, under these conditions the body was on the point of moving, determine the magnitude of 𝐹 and the normal reaction 𝑅.

  • A𝐹=157.5N, 𝑅=210N
  • B𝐹=164.06N, 𝑅=126N
  • C𝐹=157.5N, 𝑅=168N
  • D𝐹=246.09N, 𝑅=262.5N
  • E𝐹=196.88N, 𝑅=262.5N

Q10:

A body weighing 75 N rests on a rough plane inclined at an angle of 45 to the horizontal under the action of a horizontal force. The minimum horizontal force required to maintain the body in a state of equilibrium is 45 N. Find the maximum horizontal force that will also maintain the equilibrium.

This lesson includes 40 additional questions and 394 additional question variations for subscribers.

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