This set of Engineering Mechanics Multiple Choice Questions & Answers (MCQs) focuses on ” Conservative Forces”.
Explanation: The potential energy is converted into the work done. Thus is the block moves from the height h to the ground, the work done is given by . Negative because the work done is in the opposite direction of the motion of the body.
2. If any external conservative force also is applied on the distributed loading then?
a) The net force will act at the centroid of the structure only
b) The net load will not be formed as all the forces will be cancelled
c) The net force will act on the base of the loading horizontally
d) The net force will not to be considered, there would be a net force of the distribution, rest will be the external forces
Explanation: The external forces are treated differently. They are not added by the force of the distributed loading. That is the force not only acts at the centroid always. It can be shifted also. Depending on the external forces. Thus the use of centroid or centre of mass.
Explanation: First represent the forces in their vector form. Then equate the net sum of the forces in the x, y and z directions to be zero. You will get FB = FC and 2(.848) = 40N. This gives the answer as 23.6N.
4. What is the sum of squares of the cosine angles made by the conservative force vector with the coordinate axis?
Explanation: The sum of the squares of the cosines of the vector will give you the squares of the components in the numerator, and the vector’s magnitude’s square in the denominator. But the numerator sum is equal to the vector’s magnitude’s square. Thus, the answer = 1.
5. ____________ is the phenomena that resist the movement of the two surfaces in contact. This phenomenon is also having its scope in the work and the conservative nature of the force.
c) Circular movement
Explanation: The friction is the phenomena that define that there is a resistance which is present there between the two surfaces. The two surfaces are in contact and the friction applies at that surface only, resisting the motion of the surface.
6. In the explanation of the theory of friction over which conservative forces were acted upon, the block used to have an assumption. That is the upper portion of the block is considered to be rigid.
Explanation: The block used to explain the theory of friction is placed on a deformable surface. As we know that the theory of friction says that when there is no lubricating fluid present between the surfaces in contact, the dry friction occurs. Thus to show the same, experiments are done over a non-rigid/deformable surface which is having a rigid shape.
Explanation:The potential energy is converted into the work done. Thus is the block moves from the distance x2 to x1, the work done is given by . Negative because the work done is in the opposite direction of the motion of the body.
8. Which statement is right for conservative force vector F = Ai + Bj + Ck?
a) In rectangular components representation of any vector we have vector F = Ai + Bj + Ck
b) In rectangular components representation of any vector we have vector F = Ax + By + Cz
c) In rectangular components representation of any vector we have vector F = Fx + Fy + Fz
d) In rectangular components representation of any vector we have vector F = Fi + Fj + Fk
Explanation: As given the vector is F = Ai + Bj + Ck, this implies that the x ,y and z-axis components of this vector is A, B and C respectively. But, in rectangular components representation of any vector, the vector is written as F = Fx + Fy + Fz.
9. For equilibrium, the net moment acting on the body by various conservative forces is zero.
Explanation: The equilibrium is only attained if the net moment on the body tends to be equal to zero. Thus the moments caused by different forces cancel out. If this happens there is no motion of the body along any direction and hence the body is said to be in equilibrium. The body here is a rigid body.
10. Determine the horizontal components of the reaction on the beam caused by the pin at Q. The force 60N is multiplied by 10 and then is applied.
Explanation: The summation of the forces needs to be zero. So does the summation of the moments need to zero. But talking about the angles, they not needed to zero. But the forces which are acting at particular angles, must needed to.
11. The conservative frictional force always acts ____________ to the surface of the application of the friction.
Explanation: The friction is the phenomena that define that there is a resistance which is present there between the two surfaces. This friction is applied tangentially to the surfaces in contact. Thus the main thing is that the forces on both of the surfaces act as a tangential to each other.
12. What does Newton’s third law states for the conservative forces?
a) The rate of change of momentum is equal to the force applied
b) For every reaction there is an opposite reaction
c) The body is tend to be rotated if the force is applied tangentially
d) The body is rest until a force is applied
Explanation: The requirement of the third law is important in the equilibrium of the body. Specially the rigid bodies. The rigid body particles are in the equilibrium and are thus facing the forces and to be in the equilibrium they also react and apply the opposite force and thus the third law of Newton. It is the same for all the methods.
13. We use sometimes the measures to know the direction of moment in the calculations of the moments caused by the conservative forces. Which one is right about it(consider the mentioned axis to be positive)?
a) Thumb is z-axis, fingers curled from x-axis to y-axis
b) Thumb is x-axis, fingers curled from z-axis to y-axis
c) Thumb is y-axis, fingers curled from x-axis to z-axis
d) Thumb is z-axis, fingers curled from y-axis to x-axis
Explanation: As right handed coordinate system means that you are curling your fingers from positive x-axis towards y-axis and the thumb which is projected is pointed to the positive z-axis. Thus visualizing the same and knowing the basic members of the axis will not create many problems.
14. For the conditions of the equilibrium of the body, i.e. the rigid body only the external conservative forces defines the equilibrium. Because the internal conservative forces cancels out so not to be considered.
a) The first part of the statement is false and other part is true
b) The first part of the statement is false and other part is false too
c) The first part of the statement is true and other part is false
d) The first part of the statement is true and other part is true too
Explanation: The application of the internal forces does affect the conditions of the equilibrium of the body. Not only the external but the internal forces that are developed by the sake of external forces does develop a tending effect on the equilibrium of the body. Thus the internal forces doesn’t cancels out.
15. Which statement is correct about the vector F in the showing the conservative nature of the forces?
a) F= Fcos β + Fcos α + Fcosγ
b) F= Fsin β + Fcos α + Fcosγ
c) F= Fcos β + Fsin α + Fcosγ
d) F= Fcos β + Fcos α + Fsinγ
Explanation: As we know the α, β and γ are the angles made by the x, y and z-axis respectively. Thus, is the magnitude of the vector is F, the F= Fcos β + Fcos α + Fcosγ. Which means the force is the resultant of all its axis’ components.
Sanfoundry Global Education & Learning Series – Engineering Mechanics.
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