Exam 9: Static Equilibrium; Elasticity and Fracture

A 40-kg uniform ladder that is 5.0 m long is placed against a smooth wall at a height of h=4.0 m, as shown in the figure. The base of the ladder rests on a rough horizontal surface whose coefficient of static friction with the ladder is 0.40 . An 80-kg bucket is suspended from the top rung of the Iadder, just at the wall. What is the magnitude of the force that the ladder exerts on the wall?

A piano wire has a radius of 0.50 mm . One end is fixed and the other is wrapped around a tuning peg, which has a diameter of 3.5 mm and is 80 cm away. After the wire just becomes taut, the peg is given three full turns. What is the tension in the wire? Young's modulus for steel is $2.0 \times 10 ^ { 11 }$ $\mathrm { N } / \mathrm { m } ^ { 2 }$

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?

Opposing shearing forces of 3000 N are applied to the 3.00-cm x 4.00-cm faces of a metal block measuring 3.00 cm x 4.00 cm x 5.00 cm. By what distance does the block become slanted? The shear modulus for this metal is $8.10 \times 10 ^ { 10 } \mathrm {~N} / \mathrm { m } ^ { 2 }$

A steel wire, 3.2 m long, has a diameter of 1.2 mm. The wire stretches 1.6 mm when it bears a load. Young's modulus for steel is $2.0 \times 10 ^ { 11 } \mathrm {~Pa}$ The mass of the load is closest to

A 25-kg piece of equipment can be hung by steel wires of length 1.00 m, 2.00 m, or 3.00 m. If all the wires have the same diameter, which one will stretch the greatest percent?

A vertical 30-cm steel rod, 1.0 cm in diameter, supports a 300-kg mass. What is the change in Iength of the rod caused by this mass? Young's modulus for steel is $2.0 \times 10 ^ { 11 } \mathrm {~N} / \mathrm { m } ^ { 2 }$

A uniform ladder 12 meters long rests against a vertical frictionless wall, as shown in the figure. The ladder weighs 400 N and makes an angle $\theta = 51 ^ { \circ }$ with the floor. A man weighing 874 N climbs slowly up the ladder. When he is 78 m from the bottom of the Iadder, it just starts to slip. What is the coefficient of static friction between the floor and the ladder?

When a 125-kg piece of equipment is hung from a steel wire of length 75 cm, it stretches the wire by 4.00 mm . If instead the wire had a length of 150 cm, but all else were the same, by what distance would the same equipment stretch the wire?

A 320-g ball and a 400-g ball are attached to the two ends of a string that goes over a pulley with a radius of 8.7 cm. Because of friction in its axle, the pulley does not begin to rotate. What is the magnitude of the frictional torque at the axle of the pulley if the system remains at rest when the balls are released?

A store's sign has a mass of 20 kg and is 3.0 m long. It is uniform, so its center of gravity is at the center of the sign. It is supported horizontally by a small loose bolt attached to the wall at one end and by a wire at the other end, as shown in the figure. What is the tension in the wire?

A child is trying to stack two uniform bricks, each 24 cm long, so they will protrude as far as possible over the edge of a table without tipping over, as shown in the figure. What is the maximum possible overhang distance d?

A 5000-N force compresses a steel block by 0.0025 cm. How much force, applied over the same area, would be needed to compress the block by 0.0125 cm?

A 1200-kg car is being raised with a constant acceleration of $2.53 \mathrm {~m} / \mathrm { s } ^ { 2 }$ Iong steel cable that is 1.5 cm in diameter. Young's modulus for steel is $2.0 \times 10 ^ { 11 } \mathrm {~N} / \mathrm { m } ^ { 2 }$ the change in length of the cable caused by lifting the car?

A solid steel column is 4.0 m long and 0.20 m in diameter. Young's modulus for this steel is $2.0 \times$ $10 ^ { 11 } \mathrm {~N} / \mathrm { m } ^ { 2 }$ By what distance does the column shrink when a 5000-\mathrm{kg} truck is supported by it?

Tensile stress is

A cable is 100-m long and has a cross-sectional area of $1.0 \mathrm {~mm} ^ { 2 }$ stretch the cable. Young's modulus for the cable is $1.0 \times 10 ^ { 11 } \mathrm {~N} / \mathrm { m } ^ { 2 }$ stretch?

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 $7.0 \times 10 ^ { 10 } \mathrm {~N} / \mathrm { m } ^ { 2 }$

A meter stick balances at the 50.0-cm mark. If a mass of 50.0 g is placed at the 90.0-cm mark, the stick balances at the 61.3-cm mark. What is the mass of the meter stick?

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?