Exam 10: Equilibrium and Elasticity

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. The maximum mass M of the load is closest to

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 heavy boy and a lightweight girl are balanced on a massless seesaw. If they both move forward so that they are one-half their original distance from the pivot point, what will happen to the seesaw? Assume that both people are small enough compared to the length of the seesaw to be thought of as point masses.

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. By how many milliliters does this pressure reduce the volume of the oil?

A steel guitar string with a diameter of 0.300 mm and a length of 70.0 cm is stretched by 0.500 mm while being tuned. How much force is needed to stretch the string by this amount? Young's modulus for steel is 2.0 × 1011 N/m².

A cable is 100 m long, has a cross-sectional area of 1.0 mm², and is made of a material having a Young's modulus of 1.0 × 10¹¹ N/m². If a 1000-N force is applied to stretch the cable, how far does it stretch?

A 20.0-kg uniform plank is supported by the floor at one end and by a vertical rope at the other as shown in the figure. A 50.0-kg mass person stands on the plank a distance three-fourths of the length plank from the end on the floor. (a) What is the tension in the rope? (b) What is the magnitude of the force that the floor exerts on the plank?

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?

A 5.0-m long, 12-kg uniform ladder rests against a smooth vertical wall with the bottom of the ladder 3.0 m 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 60-kg person climb before the ladder starts to slip?

A 0.600-mm diameter wire stretches 0.500% of its length when it is stretched with a tension of 20.0 N. What is the Young's modulus of this wire?

A nonuniform, 80.0-g, meterstick balances when the support is placed at the 51.0-cm mark. At what location on the meterstick should a 5.00-g tack be placed so that the stick will balance at the 50.0 cm mark?

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.

The graph in the figure shows the force on an object as a function of the elongation caused by that force. Which statement about this object is true?

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?

What is the maximum length of a metal cable that can hang vertically supported from one end of the cable? The Young's modulus of this metal is 2.10 × 10¹¹ N/m², its tensile strength (the maximum tensile stress it can support without breaking) is 7.40 × 10⁸ N/m², and its density is 7.60 × 10³ kg/m³.

A very light 1.00-m wire consists of two segments of equal length, one of steel (Young's modulus is 2.00 × 10¹¹ N/m²) and one of brass (Young's modulus is 9.0 × 1010 N/m²). The steel segment is 1.50 mm in diameter, and the brass segment has twice this diameter. When a weight w is hung from the ceiling by this wire, the steel segment stretches by 1.10 mm. By what distance does the brass segment stretch?

Tensile stress is

If the torque on an object adds up to zero

In the figure, a uniform ladder 12 meters long rests against a vertical frictionless wall. The ladder weighs 400 N and makes an angle θ of 79° with the floor. A man weighing 790 N climbs slowly up the ladder. When he has climbed to a point that is 7.8 m from the base of the ladder, the ladder starts to slip. What is the coefficient of static friction between the floor and the ladder?