# 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 to the horizontal. If the coefficient of friction between the body and the plane is , 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 , find the magnitude of the limiting friction. • A46 N
• B N
• C23 N
• D N

Q3:

A body weighing 60 N rests on a rough plane inclined to the horizontal at an angle whose sine is . 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.

• A
• B
• C
• D
• E

Q4:

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

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. • A
• B
• C
• D

Q6:

A body of weight 438 N rests on a rough plane inclined at an angle of to the horizontal. The coefficient of friction between the body and the plane is . 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 to the horizontal. The body is pulled upward by a string making an angle of to the line of greatest slope of the plane. When the tension in the string is N, the body is on the point of moving up the plane. Find the coefficient of friction between the body and the plane.

• A
• B
• C
• D

Q8:

A body weighing 56 N rests on a rough plane inclined at an angle of to the horizontal. The coefficient of friction between the body and the plane is . The body is pulled upward by a string making an angle of 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.

• A N
• B N
• C N
• D56 N
• E 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 , it was on the point of moving. The same body was later placed on a horizontal surface of the same roughness. A force acted on the body pulling upward at an angle of to the horizontal where . Given that, under these conditions the body was on the point of moving, determine the magnitude of and the normal reaction .

• A,
• B,
• C,
• D,
• E,

Q10:

A body weighing 75 N rests on a rough plane inclined at an angle of 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.