Statics — Quiz 1

Questions in this quiz (10)

1. A composite area consists of a rectangle $$8\ m$$ wide and $$5\ m$$ tall with a circular hole of diameter $$3\ m$$. The center of the hole is located at $$\left(5\ m,2.5\ m\right)$$ from the bottom-left corner of the rectangle. Determine the $$x$$-coordinate of the centroid of the composite area.

   • $$3.79\ m$$
   • $$4.12\ m$$
   • $$4.36\ m$$
   • $$4.58\ m$$

2. A rectangular cross-section has a width of $$150\ mm$$ and a height of $$400\ mm$$. Determine the area moment of inertia about the horizontal centroidal axis.

   • $$800\times10^6\ mm^4$$
   • $$600\times10^6\ mm^4$$
   • $$320\times10^6\ mm^4$$
   • $$1200\times10^6\ mm^4$$

3. A $$60$$-kg block rests on a plane inclined at $$25^\circ$$ to the horizontal. The coefficient of static friction between the block and the plane is $$0.45$$. Determine the friction force acting on the block when it is in equilibrium. Assume $$g=9.81\ m/s^2$$.

   • $$231.2\ N$$
   • $$240.1\ N$$
   • $$269.1\ N$$
   • $$298.6\ N$$

4. Two parallel forces of equal magnitude $$120\ N$$ act in opposite directions. The perpendicular distance between the forces is $$2.5\ m$$. Determine the magnitude of the couple moment.

   • $$150\ N\cdot m$$
   • $$240\ N\cdot m$$
   • $$300\ N\cdot m$$
   • $$600\ N\cdot m$$

5. A beam is supported by a pin at point $$A$$ and a roller at point $$B$$. The distance between supports is $$6\ m$$. A vertical load of $$10\ kN$$ is applied at a point $$2\ m$$ from support $$A$$. Determine the vertical reaction at support $$A$$.

   • $$3.3\ kN$$
   • $$4.0\ kN$$
   • $$5.0\ kN$$
   • $$6.7\ kN$$

6. In a truss, three members meet at a joint with no external load. Two of the members are collinear. Which statement best describes the third member?

   • It carries the same force as the collinear members
   • It carries zero force
   • It carries the largest force in the truss
   • It carries half the force of the collinear members

7. A $$90$$-kg block rests on a horizontal surface with a coefficient of static friction $$\mu_s=0.30$$. A force is applied at an angle of $$30^\circ$$ above the horizontal. Determine the minimum force required to start motion. Assume $$g=9.81\ m/s^2$$.

   • $$261\ N$$
   • $$332\ N$$
   • $$365\ N$$
   • $$412\ N$$

8. A rectangular cross-section has dimensions $$200\ mm$$ by $$120\ mm$$. Using the parallel axis theorem, determine the moment of inertia about an axis parallel to the centroidal horizontal axis located $$100\ mm$$ away.

   • $$75.2\times10^6\ mm^4$$
   • $$92.4\times10^6\ mm^4$$
   • $$108.6\times10^6\ mm^4$$
   • $$268.8\times10^6\ mm^4$$

9. An $$L$$-shaped cross-section is formed by two rectangles. The vertical leg is $$50\ mm$$ wide and $$120\ mm$$ tall. The horizontal leg is $$100\ mm$$ wide and $$50\ mm$$ tall, extending to the right from the bottom of the vertical leg. The two rectangles share a $$50\ mm\times50\ mm$$ square region. Determine the $$y$$-coordinate of the centroid measured from the bottom.

   • $$36.2\ mm$$
   • $$42.5\ mm$$
   • $$49.7\ mm$$
   • $$55.0\ mm$$

10. A force system consists of a single force of $$600\ N$$ and a couple moment of $$900\ N\ m$$. The system is replaced by an equivalent single force. Determine the perpendicular distance from the original line of action to the new line of action.

    • $$0.75\ m$$
    • $$1.25\ m$$
    • $$1.50\ m$$
    • $$2.00\ m$$