6. Intro to Forces (Dynamics)

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 75-kg petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 62 kg. How might the thief use this 'rope' to escape? Give a quantitative answer.

A window washer pulls herself upward using the bucket–pulley apparatus shown in Fig. 4–40. If she increases this force by 15%, what will her acceleration be? The mass of the person plus the bucket is 78 kg.

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(II) One 3.2-kg paint bucket is hanging by a massless cord from another 3.2-kg paint bucket, also hanging by a massless cord, as shown in Fig. 4–41. If the buckets are at rest, what is the tension in each cord?

III) Determine a formula for the magnitude of the force $\overrightarrow{F}$ exerted on the large block (m_C) in Fig. 4–56 so that the mass m_A does not move relative to m_C. Ignore all friction. Assume m_B does not make contact with m_C.

(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.]

A coffee cup on the horizontal dashboard of a car slides forward when the driver decelerates from 45 km/h to rest in 3.5 s or less, but not if she decelerates in a longer time. What is the coefficient of static friction between the cup and the dash? Assume the road and the dashboard are level (horizontal).