Exam 11: Equilibrium and Elasticity

An 82.0 kg-diver stands at the edge of a light 5.00-m diving board,which is supported by two narrow pillars 1.60 m apart,as shown in the figure.Find the magnitude and direction of the force exerted on the diving board (a)by pillar A. (b)by pillar B.

Tensile strain is

The tensile strength (the maximum tensile stress it can support without breaking)for a certain steel wire is 3000 MN/m².What is the maximum load that can be applied to a wire with a diameter of 3.0 mm made of this steel without breaking the wire?

A 3.00-kg ball rests in a frictionless groove as shown in the figure. (a)What is the magnitude of the force that the left side of the groove exerts on the ball? (b)What is the magnitude of the force that the right side of the groove exerts on the ball?

The base of an aluminum block,which is fixed in place,measures 90 cm by 90 cm,and the height of the block is 60 cm.A force,applied to the upper face and parallel to it,produces a shear strain of 0.0060.The shear modulus of aluminum is Pa.What is the sheer stress on the block?

If the torque on an object adds up to zero

In the figure,a uniform rectangular crate 0.40 m wide and 1.0 m tall rests on a horizontal surface.The crate weighs 930 N,and its center of gravity is at its geometric center.A horizontal force F is applied at a distance h above the floor.If what minimum value of F is required to make the crate start to tip over? Static friction is large enough that the crate does not start to slide.

A copper sphere has a radius of 2.50 m under normal room pressure of 1.0 × 10⁵ N/m².If we increase the pressure on this sphere to 10 times the normal room pressure,what is the change in its volume? The bulk modulus for copper is 1.4 × 10¹¹ Pa.

Two identical ladders are 3.0 m long and weigh 600 N each.They are connected by a hinge at the top and are held together by a horizontal rope,1.0 m above the smooth floor forming a symmetric "A" arrangement.The angle between the ladders is 60° and both ladders have their center of gravity at their midpoint.What is the tension in the rope?

A stepladder consists of two halves,hinged at the top,and connected by a tie rod that keeps the two halves from spreading apart.In this particular instance,the two halves are 2.50 m long,the tie rod is connected to the center of each half and is 70.0 cm long.An 800-N person stands 3/5 of the way up the stepladder,as shown in the figure.Neglecting the weight of the ladder,and assuming that the ladder is resting on a smooth floor,what is the tension in the tie rod? Note: To solve this problem you must "cut" the ladder in half and consider the equilibrium of forces and torques acting on each half of the ladder.

When the pressure applied to an unknown liquid is increased from to ,the volume of the liquid decreases by 0.70%.Calculate the bulk modulus of the liquid.

A 5.0-m long,12-kg uniform ladder rests against a smooth vertical wall with the bottom of the ladder from the wall.The coefficient of static friction between the floor and the ladder is 0.28.What distance,measured along the ladder from the bottom,can a person climb before the ladder starts to slip?

A sample of tendon 3.00 cm long and 4.00 mm in diameter is found to break under a minimum force of 128 N.If instead the sample had been 1.50 cm long and of uniform composition and cross-sectional area,what minimum force would have been required to break it?

A 12-L volume of oil is subjected to a pressure change,which produces a volume strain on the oil of -3.0 × 10^-4.The bulk modulus of the oil is 6.0 × 10⁹ N/m² and is independent of the pressure.What is the pressure change that produced the volume strain in the oil?

A 12-L volume of oil is subjected to a pressure change,which produces a volume strain on the oil of .The bulk modulus of the oil is and is independent of the pressure.By how many milliliters does this pressure reduce the volume of the oil?

A 20.0-kg uniform door has a width of 1.20 m and a height of 2.50 m.The door is mounted on a post by a pair of hinges,marked 1 and 2 in the figure,at the top and bottom of the door.An external force of 60.0 N,at an angle of 30.0° above the horizontal,is applied to the small doorknob,as shown in the figure.The doorknob is 1.00 m above the bottom of the door. (a)Find the x component of the force that hinge 1 exerts on the door at the top. (b)Find the SUM of the y components of the forces that hinges 1 and 2 together exert on the door.

A uniform 300-kg beam,6.00 m long,is freely pivoted at P,as shown in the figure.The beam is supported in a horizontal position by a light strut,5.00 m long,which is freely pivoted at Q and is loosely pinned to the beam at R.A load of mass is suspended from the end of the beam at S.A maximum compression of 23,000 N in the strut is permitted,due to safety.Under maximum load,find the magnitude of the x component of the force exerted on the beam by the pivot at P.

Tensile stress is

A shear force of 400 N is applied to one face of an aluminum cube with sides of 30 cm while the opposite face is held fixed in place.What is the resulting displacement of the face? (The shear modulus for aluminum is 2.5 × 10¹⁰ N/m²)

An aluminum wire and a steel wire,each of length 2.0 m,are hung from the ceiling.A mass is suspended from the lower end of each wire.The aluminum wire has a diameter of .What must be the diameter of the steel wire if it is to stretch the same distance as the aluminum wire,so that the two wires maintain equal lengths after the masses are attached? Young's modulus for aluminum is and for steel it is .