6. Intro to Forces (Dynamics)

A force of magnitude $10$ N acts at an angle of $30°$ above the positive x-axis. What are the x and y components of this force?

A uniform rectangular gate of width $w$ and height $h$ is submerged vertically in water with its top edge at the water surface. What is the magnitude and direction of the force that must be applied horizontally at the bottom of the gate to keep it in equilibrium against the hydrostatic force of the water?

A boat is anchored in a river where the current exerts a force of $500N$ downstream. If the anchor rope makes an angle of $30°$ with the riverbed and holds the boat stationary, what is the magnitude and direction of the anchoring force exerted by the rope?

Which of the following best describes the shape of the shear force diagram for a simply supported beam of length $L$ subjected to a single concentrated load $P$ at its midpoint, following the standard sign convention (positive shear causes clockwise rotation of the segment on which it acts)?

Which of the following best describes the shape of the bending moment diagram for a simply supported beam subjected to a uniformly distributed load along its entire length?

A $20 \mathrm{kg}$ box is suspended at rest by a vertical strap. To what tension must the strap be adjusted to provide the necessary upward force to keep the box stationary? (Assume $g=9.8 m/s^2$.)

A particle moves along the x-axis under the influence of a force $F_x$ that varies with position as shown in the figure. Which of the following statements is correct about the work done by the force as the particle moves from $x=0$ to $x=5$ meters?

Two forces, $F_1$ and $F_2$, act on an object at angles ${\theta }_1$ and ${\theta }_2$ with respect to the x-axis. What is the x component of the resultant force?

Which of the following statements correctly describes the force diagram for an object at rest on a horizontal surface?

A girl with a weight of $200-N$ stands stationary on a weighing scale. What is the magnitude of the support force exerted by the scale on the girl?

What is responsible for the apparent change in weight that riders experience on roller coasters?

A box is being pulled to the right with a force of $10N$ and to the left with a force of $4N$. What is the magnitude and direction (right or left) of the net force acting on the box?

Three identical bricks are placed in a row on a frictionless surface. A hand pushes only the first brick to the right, causing all three bricks to accelerate together. Which statement best describes the magnitude of the force that the second brick exerts on the third brick compared to the force that the hand exerts on the first brick?

Three ropes are tied to a small ring and pull on it with forces in different directions. If the ring remains at rest, which of the following statements is true about the vector sum of the forces acting on the ring?

A simple truss is constructed in the shape of an equilateral triangle with each side of length $L$. A load of $P$ is applied vertically downward at the top vertex. Assuming all joints are pin-connected and the truss is supported at the two base vertices, which of the following gives the magnitude of the force in each of the two base members?