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Engineering Mechanics Test 1
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Engineering Mechanics Test 1
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  • Question 1/15
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    The resultant of two forces P and Q (such that P > Q) acting along the same straight line, but in opposite direction, is given by
    Solutions

    Resultant Force R is given by:

    P and Q are acting on same line but in opposite direction so θ = 180°

  • Question 2/15
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    The angle between two forces when the resultant is maximum and minimum respectively are
    Solutions

    Resultant force is a single force which produces the same effect as produced by all the given forces acting on a body.

    When θ = 0°

    When θ = 90°

    When θ = 180°

    So resultant force R will be maximum when θ = 0° and minimum when θ = 180°
  • Question 3/15
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    According to Lami’s theorem
    Solutions

    LAMI’S Theorem states, “If three coplanar forces acting at a point be in equilibrium, then each force is proportional to the sine of the angle between the other two.” Mathematically,

  • Question 4/15
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    A force while acting on a body may
    Solutions

    Force

    It may be defined as an agent which produces or tends to produce, destroy or tends to destroy the motion of a body. A force while acting on a body may

    a) change the motion of a body,

    b) retard the motion of body,

    c) balance the forces already acting on a body, and

    d) give rise to the internal stresses in a body

    In order to determine the effects of a force acting on a body, we must know the following characteristics of a force

    i) The magnitude of the force,

    ii) The line of action of the force,

    iii) The nature of the force, i.e. push or pull, and

    iv) The point at which the force is acting
  • Question 5/15
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    Two like parallel forces P and Q (P > Q) act on a rigid body. If the force P is displaced parallel to itself through a distance d, then the resultant of the forces P and Q would be shifted by a distance
    Solutions

    When P is shifted by d, let R is shifted by a.

    P + Q = R

    Pd1 = Qd2

    P (d1 – d + a) = Q (d2 – a)

    Pd1 – Pd + Pa = Qd2 – Qa

    Pd – Pa = Q a

    Pd = (Q + P) a

  • Question 6/15
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    A smooth cylinder lying on a convex surface remains in ________ equilibrium.
    Solutions

    A body is said to be in equilibrium when it comes back to its original position after it is slightly displaced from its position of rest. In general, the following are the three types of equilibrium :

    Stable equilibrium:

    • A body is said to be in stable equilibrium if it returns back to its original position after it is slightly displaced from its position of rest
    • This happens when some additional force sets up due to displacement and brings the body back to its original position
    • A smooth cylinder, lying in a curved surface, is in stable equilibrium

    Unstable equilibrium

    • A body is said to be in an unstable equilibrium if it does not return back to its original position, and heels farther away after slightly displaced from its position of rest
    • This happens when the additional force moves the body away from its position of rest
    • A smooth cylinder lying on a convex surface 

    Neutral equilibrium

    • A body is said to be in a neutral equilibrium, if it occupies a new position (and remains at rest in this position) after slightly displaced from its position of rest
    • This happens when no additional force sets up due to the displacement
    • A smooth cylinder lying on a horizontal plane is in neutral equilibrium

     

  • Question 7/15
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    The forces, which meet at one point and their lines of action also lie on the same plane, are known as
    Solutions

    When two or more forces act on a body, they are called to form a system of forces.

    Coplanar forces: The forces, whose lines of action lie on the same plane, are known as coplanar forces.

    Collinear forces: The forces, whose lines of action lie on the same line, are known as collinear forces.

    Concurrent forces: The forces, which meet at one point, are known as concurrent forces. The concurrent forces may or may not be collinear.

    Coplanar concurrent forces: The forces, which meet at one point and their lines of action also lie on the same plane, are known as coplanar concurrent forces.

    Coplanar non-concurrent forces: The forces, which do not meet at one point, but their lines of action lie on the same plane, are known as coplanar non-concurrent forces.

    Non-coplanar concurrent forces: The forces, which meet at one point, but their lines of action do not lie on the same plane, are known as non-coplanar concurrent forces.

    Non-coplanar non-concurrent forces: The forces, which do not meet at one point and their lines of action do not lie on the same plane, are called non-coplanar non-concurrent forces.

  • Question 8/15
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    A system of forces is acting at the corners of a rectangular block as shown in figure. Determine the magnitude of the resultant force.

    Solutions

    Given: System of forces

    Magnitude of the resultant force

    Resolving forces horizontally,

    ΣH = 25 - 20 = 5 kN

    and now resolving the forces vertically

    ΣV = (-50) + (-35) = -85 kN

    ∴ Magnitude of the resultant force

  • Question 9/15
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    If a rigid body is in equilibrium under the action of three forces, then
    Solutions

    Principles of equilibrium

    1. Two force principle: If only two forces act on a body that is in equilibrium, then they must be equal in magnitude, co-linear and opposite in sense.

    2. Three force principle: If a body in equilibrium is acted upon by three forces, then the resultant of any two forces must be equal, opposite and collinear with the third force. If a three-force member is in equilibrium and the forces are not parallel, they must be concurrent. Therefore, the lines of action of all three forces acting on such a member must intersect at a common point; any single force is, therefore, the equilibrant of the other two forces.

    If it does not pass through a common point, it will produce a couple.

     

    A solid body applied to three forces whose lines of action are not parallel, is in equilibrium if the three following conditions satisfies:

    (i). The lines of action are coplanar (in the same plane).

    (ii). The lines of action are meeting at a point.

    (iii). The vector sum of these forces is equal to the zero vector.

    3. Four force principle: If a body in equilibrium is acted upon by four forces, then the resultant of any two forces must be equal, opposite and collinear with the resultant of the other two forces.
  • Question 10/15
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    A weight W hangs by a string. It is pushed aside by a horizontal force until the string makes an angle of 30° with the vertical. The tension in the string is
    Solutions

    T cos 30° = W

  • Question 11/15
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    The resultant of the forces P and Q is R. If Q is doubled then R gets doubled in magnitude. R is again doubled if Q is reversed. Then P2, Q2 and R2 are in the ratio
    Solutions

    When Q’=2Q then R’ = 2R

    When Q’ = -Q then R’ = 2R

    By Subtracting both the equations :

    By adding both the equations :

  • Question 12/15
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    The moment of the force P about O as shown in figure is

    Solutions

    Moment of a Force

    Moment of a force about a point is the measure of rotational effect of the force. Moment of a force about a point is defined as the product of the magnitude of the force and the perpendicular distance of the point from the line of action of the force. The point about which the moment is considered is called moment centre and the perpendicular distance of the point from the line of action of the force is called moment arm.

    Here d1 is the perpendicular distance of point 1 from the line of action of force F, the moment of F about point 1 is given by

    M1 = Fd1

    Similarly, M2 = Fd2

    Moment of the force P about O = P × OC = AB × OC

  • Question 13/15
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    Which of the following statement is correct?
    Solutions

    A pair of two equal and unlike parallel forces (i.e. forces equal in magnitude, with lines of action parallel to each other and acting in opposite directions) is known as a couple.

    As a matter of fact, a couple is unable to produce any translatory motion (i.e., motion in a straight line). But it produces a motion of rotation in the body, on which it acts.

    Moment of a couple = P × a

    Characteristics of a couple

    A couple (whether clockwise or anticlockwise) has the following characteristics:

    1. The algebraic sum of the forces, constituting the couple, is zero.

    2. The algebraic sum of the moments of the forces, constituting the couple, about any point is the same, and equal to the moment of the couple itself.

    3. A couple cannot be balanced by a single force. But it can be balanced only by a couple of opposite sense.

    4. Any no. of co-planer couples can be reduced to a single couple, whose magnitude will be equal to the algebraic sum of the moments of all the couples.
  • Question 14/15
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    The force induced in the string BC due to the load W as shown in figure is

    Solutions

    FAB sin θ = W

    FAB = W cosec θ

    FBC = FAB cos θ = W cosec θ × cos θ

  • Question 15/15
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    Two like parallel forces are acting at a distance of 24 mm apart and their resultant is 20 N. If the line of action of the resultant is 6 mm from any given force, the two forces are
    Solutions

    As these are like parallel forces so F1 + F2 = 20 N

    Taking moment about point of action of Resultant force R:

    F1 × 18 = F2 × 6

    F2 = 3F1

    F1 + F2 = 20

    4F1 = 20 ⇒ F1 = 5 N ⇒ F2 = 15 N
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