Statics — Quiz 2

Questions in this quiz (10)

1. A rectangular plate $$18\ m\times12\ m$$ has a circular hole of radius $$3\ m$$ removed. The center of the hole is located at coordinates $$\left(13\ m,8\ m\right)$$ from the bottom-left corner. Determine the $$x$$-coordinate of the centroid of the remaining area.

   • $$9.10\ m$$
   • $$8.40\ m$$
   • $$9.60\ m$$
   • $$8.00\ m$$

2. A load of $$20\ kN$$ is supported by a horizontal strut and a cable inclined at $$40^\circ$$ above the horizontal. Determine the tension in the cable.

   • $$31.1\ kN$$
   • $$26.1\ kN$$
   • $$20.0\ kN$$
   • $$15.3\ kN$$

3. A pulley with radius $$0.5\ m$$ has a belt with tensions of $$900\ N$$ on the tight side and $$400\ N$$ on the slack side. Determine the net torque acting on the pulley.

   • $$250\ N\cdot m$$
   • $$350\ N\cdot m$$
   • $$500\ N\cdot m$$
   • $$650\ N\cdot m$$

4. A hollow square cross-section has outer dimensions $$120\ mm\times120\ mm$$ and inner dimensions $$80\ mm\times80\ mm$$. Determine the radius of gyration about the centroidal axis.

   • $$35.2\ mm$$
   • $$41.63\ mm$$
   • $$46.8\ mm$$
   • $$52.1\ mm$$

5. In mechanism analysis using the instant center method, what does the instant center represent?

   • The location where all velocities are zero
   • The point about which a body undergoes instantaneous rotation
   • The center of mass of the moving body
   • The point where acceleration becomes zero

6. Four concurrent forces act at a point: $$120\ N$$ at $$0^\circ$$, $$160\ N$$ at $$60^\circ$$, $$140\ N$$ at $$180^\circ$$, and $$100\ N$$ at $$270^\circ$$. Angles are measured from the positive $$x$$-axis. Determine the magnitude of the resultant force.

   • $$71.3\ N$$
   • $$138.9\ N$$
   • $$176.5\ N$$
   • $$214.4\ N$$

7. A simply supported beam has a span of $$10\ m$$. Using influence lines, determine the reaction at the left support when a unit load is placed $$3\ m$$ from the left support.

   • $$0.3$$
   • $$0.7$$
   • $$0.5$$
   • $$0.6$$

8. A planar truss has $$12$$ members, $$8$$ joints, and $$3$$ reaction components. Determine the static classification of the truss.

   • Stable and statically determinate
   • Indeterminate to the first degree
   • Indeterminate to the second degree
   • Unstable

9. A solid cylinder with mass $$25\ kg$$ and radius $$0.25\ m$$ rolls down an incline at $$30^\circ$$. The coefficient of static friction is $$0.30$$. Determine the friction force acting on the cylinder. Assume $$g=9.81\ m/s^2$$.

   • $$26\ N$$
   • $$41\ N$$
   • $$56\ N$$
   • $$74\ N$$

10. A beam is supported by a spring with stiffness of $$400\ kN/m$$. A concentrated load of $$20\ kN$$ is applied at the spring location. Determine the deflection of the spring.

    • $$25\ mm$$
    • $$12.5\ mm$$
    • $$40\ mm$$
    • $$50\ mm$$