Exam 8: Equilibrium Ad Elasticity

To determine the location of the center of mass (or center of gravity)of a car, the car is driven over a scale on a horizontal floor. When the front wheels are over the scale, the weight recorded by the scale is 5800 N, and when the rear wheels are over the scale, the scale reads 6500 N. The distance between the front and rear wheels is measured to be 3.20 m. How far behind the front wheels is the center of mass located?

A 3.00-m-long ladder, weighing 200 N, leans against a smooth vertical wall with its base on a horizontal rough floor, a distance of 1.00 m away from the wall. The ladder is not completely uniform, so its center of gravity is 1.20 m from its base. What force of friction must the floor exert on the base of the ladder to prevent the ladder from sliding down?

A uniform 1200-N piece of medical apparatus that is 3.5 m long is suspended horizontally by two vertical wires at its ends. A small but dense 550-N weight is placed on the apparatus 2.0 m from one end, as shown in the figure. What are the tensions, A and B, in the two wires?

As shown in the figure, a 10.0 m long bar is attached by a frictionless hinge to a wall and held horizontal by a light rope that makes an angle ? = 49° with the bar. The bar is uniform and weighs $66.5 \mathrm {~N}$ What distance x from the hinge should a 10.0 kg mass be suspended for the tension in the rope to be 177 N?

A large 75-kg lighting fixture can be hung from wires of identical size and shape made of aluminum, brass, or copper. The values of Young's modulus for these metals are 0.70 × 10¹¹ Pa (aluminum), 0.91 × 10¹¹ (brass), and 1.1 × 10¹¹ (copper). Which wire would stretch the least distance?

A 50-kg air conditioner is placed on top of a concrete pad that is 20 cm thick and has a cross-sectional area of 3.0 m². What is the change in thickness of the pad caused by the air conditioner? Young's modulus for concrete is 2.3 × 10¹⁰ N/m².

An 82-kg painter stands on a long horizontal board 1.55 m from one end. This 27-kg board is uniform, 5.5 m long, and supported at each end by vertical posts. (a)What is the magnitude of the total force provided by both posts? (b)With what force does the post that is closest to the painter push upward on the board?

As shown in the figure, a uniform rectangular crate 0.40 m wide and 1.0 m tall sits on a horizontal surface. The crate weighs 460 N, and its center of gravity is at its geometric center. A horizontal force of magnitude F is applied at a distance h above the floor. Friction at the floor is great enough to prevent the crate from sliding. If $h = 0.69 \mathrm {~m}$ what minimum value of F is required to make the crate start to tip over?

A very light ideal spring having a spring constant (force constant)of 8.2 N/cm is used to lift a 2.2-kg tool with an upward acceleration of 3.25 m/s². If the spring has negligible length when it us not stretched, how long is it while it is pulling the tool upward?

A croquet mallet balances when suspended from its center of mass, as shown in the left part of the figure. If you cut the mallet into two pieces at its center of mass, as shown in the right part of the figure, how do the masses of the two pieces compare? (There could be more than one correct choice.)

Tensile stress is

If an object remains at rest, then the sum of both the external torques and the external forces on the object must be zero.

As one stretches a metal wire, which condition is reached first?

An aluminum wire 2.0 m long and 2.0 mm in diameter supports a 10.0-kg fixture. What is the stress in the wire? Young's modulus for aluminum is 7.0 × 10¹⁰ N/m².

An ornament of mass 40.0 g is attached to a vertical ideal spring with a force constant (spring constant)of 20.0 N/m. The ornament is then lowered very slowly until the spring stops stretching. How much does the spring stretch?

The mobile shown in the figure is perfectly balanced, and the horizontal supports have insignificant masses. What must be the masses of the suspended objects m₁, m₂, and m₃ to maintain balance?

When a 125-kg piece of equipment is hung from a steel wire of diameter 6.00 mm, it stretches the wire by 4.00 mm. If instead the wire had a diameter of 3.00 mm, but all else were the same, by what distance would the same equipment stretch the wire?

A mobile is shown in the figure. The horizontal supports have negligible mass. Assume that all the numbers given in the figure are accurate to two significant figures. What mass M is required to balance the mobile?

An athlete holds a 7.5-kg shot put in his hand with his lower arm horizontal, as shown in the figure. His lower arm has a mass of 2.8 kg and its center of gravity (or center of mass)is 12 cm from the elbow-joint pivot. How much force must the extensor muscle (which is $\overrightarrow { \mathrm { F } }$ _M in the figure)in the upper arm exert on the lower arm?

A uniform 40-N board supports two children weighing 500 N and 350 N. If the support is at the center of the board and the 500-N child is 1.5 m from its center, how far is the 350-N child from the center?