6. Intro to Forces (Dynamics)

The double Atwood machine shown in Fig. 4–55 has frictionless, massless pulleys and cords. Determine the tensions F_TA and F_TC in the cords.

A 2.0-m-long, 500 g rope pulls a 10 kg block of ice across a horizontal, frictionless surface. The block accelerates at 2.0 m/s². How much force pulls forward on he rope? Assume that the rope is perfectly horizontal.

In a system where a bent rod is supported at points $a$, $b$, and $c$ by smooth journal bearings as shown in Figure 1, which of the following statements best describes the types of forces and moments that the bearings can support at these points?

In the loaded truss shown, member $BE$ is subjected to forces due to the applied loads and the reactions at the supports. If the truss is in static equilibrium and all joints are pin-connected, which of the following best represents the force in member $BE$?

Consider a simple truss consisting of three members forming a right triangle: member $AB$ is horizontal, member $AC$ is vertical, and member $BC$ is the hypotenuse. A load of $1000N$ is applied downward at joint $C$. If the truss is supported at $A$ (pinned) and $B$ (roller), which statement correctly describes the forces in members $AB$, $AC$, and $BC$, and whether they are in tension or compression?

Two objects of masses $m_1$ and $m_2$ are connected by a massless string and placed on a frictionless horizontal surface. If a horizontal force $F$ is applied to $m_1$, what is the tension in the string between the objects?

Which two external forces most commonly act on darts as they travel toward a dartboard?

(III) The two masses shown in Fig. 4–57 are each initially 1.8 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its 'launch' speed. Assume the mass doesn't hit the pulley or the ceiling. Ignore the mass of the cord.]

An L-shaped object consists of three point masses, each of mass $m$, connected by light rods to form a right angle. If the lengths of the rods are $a$ and $b$, what is the moment of inertia of the system about an axis perpendicular to the plane and passing through the vertex of the L-shape?

In the truss shown, member $BD$ is connected to joints $B$ and $D$, and the truss is supported by a pin at $C$ and a roller at $A$. If a downward load of $10 \mathrm{kN}$ is applied at joint $B$, what is the force in member $BD$ and the horizontal and vertical components of the reaction at support $C$?

For the cantilever beam of length $L$ fixed at one end and subjected to a downward point load $F$ at its free end, what is the magnitude of the reaction force at the fixed support?

A rigid beam is supported by a pin at point C and an $A-36$ steel guy wire AB. If a downward force of $10 \mathrm{kN}$ is applied at the end of the beam, which of the following best describes the role of the guy wire AB in the system?

Three $250g$ masses are connected by massless, rigid rods to form a straight line and are suspended horizontally. If the system is in equilibrium and the tension in the leftmost rod is $T$, what is the value of $T$ in newtons? (Assume $g=9.8m/s^2$.)

A 500 kg air conditioner sits on the flat roof of a building. The coefficient of static friction between the roof and the air conditioner is 0.90. A massless rope attached to the air conditioner passes over a massless, frictionless pulley at the edge of the roof. In an effort to drag the air conditioner to the edge of the roof, four 100 kg students hang from the free end of the rope, but the air conditioner refuses to budge. What is the magnitude of the rope tension at the point where it is attached to the air conditioner?