Exam 8: Equilibrium Ad Elasticity

A light board that is 10 m long is supported by two sawhorses, one at one end of the board and a second at the midpoint. A 40-N object is placed between the two sawhorses, 3.0 m from the end and 2.0 m from the center. A second object, with a weight of 15 N, is placed on the supported end. What magnitude forces do the sawhorses exert on the board?

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 × 10¹¹ N/m².

A bridge piling has a cross-sectional area of 1.250 m² and supports a load of 1875 N. What is the stress on the column?

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 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?

A 50-kg bucket of concrete is suspended from a steel wire that is 1.0 mm in diameter 1.0 mm and 11.2 m long. What distance will the wire stretch? Young's modulus for steel is 2.0 x 10¹¹ Pa.

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 magnitude of the net force that the bolt exerts on the sign?

An irregularly shaped object that is 10 m long is placed with each end on a scale. If the scale on the right reads $96 \mathrm {~N}$ while the scale on the left reads $71 \mathrm {~N}$ how far from the left end is the center of gravity of this object?

A cable is 100-m long and has a cross-sectional area of 1.0 mm². A 1000-N force is applied to stretch the cable. Young's modulus for the cable is 1.0 × 10¹¹ N/m². How far does the cable stretch?

An object attached to a spring is pulled across a horizontal frictionless surface. If the force constant (spring constant)of the spring is 45 N/m and the spring is stretched by 0.88 m when the object is accelerating at $1.4 \mathrm {~m} / \mathrm { s } ^ { 2 }$ what is the mass of the object?

The graph in the figure shows the tensile stress as a function of the tensile strain in a certain wire. What does the slope of this graph give us for this wire?

A 15-kg child is sitting on a playground teeter-totter, 1.5 m from the pivot. What is the minimum distance, on the other side of the pivot, such that a 220-N force will make the child lift off the ground?

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

Tensile strain is

A very light ideal spring of spring constant (force constant)2.5 N/cm is 15 cm long when nothing is attached to it. It is now used to pull horizontally on a 12.5-kg box on a perfectly smooth horizontal floor. You observe that the box starts from rest and moves 96 cm during the first 1.6 s of its motion with constant acceleration. How long is the spring during this motion?

A wire of diameter 0.20 mm stretches by 0.20% when a 6.28-N force is applied to it. What is Young's modulus for this wire?

A 100-kg nonuniform boom that is 6.0 m long is loosely pinned at the pivot at P. A 600-kg concrete block is suspended from the end of the boom at A, as shown in the figure. The boom forms a 30° angle above the horizontal, and is supported by a 4.0-m cable between points D and B. Point B is 4.0 m from P, and point D is 4.0 m above P. The center of mass of the boom is at point C, which is 2.0 m from P. Assume that all the quantities shown in the figure are accurate to two significant figures. What is the tension in the cable connected between points B and D?

When a car is weighed, it is driven slowly on a horizontal floor over a scale that records a reading as the front wheels go over the scale, and then records a second reading as the rear wheels go over the scale. The weight of the car is equal to

Which one of the following is an accurate statement?

A very light ideal spring with a spring constant (force constant)of 2.5 N/cm pulls horizontally on an 18-kg box that is resting on a horizontal floor. The coefficient of static friction between the box and the floor is 0.65, and the coefficient of kinetic friction is 0.45. (a)How long is the spring just as the box is ready to move? (b)If the spring pulls the box along with a constant forward velocity of 1.75 m/s, how long is the spring? (c)How long is the spring if it pulls the box forward at a constant 2.75 m/s?