Exam 8: Extended Bodies at Rest

A 10-m uniform beam weighing 100 N is supported by two vertical ropes at its ends.If a 400-N person sits at a point 2.0 m from the left end of the beam,what is the force that each rope exerts on the beam?

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?

A 120-kg refrigerator that is 2.0 m tall and 85 cm wide has its center of mass at its geometrical center.You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator.The coefficient of static friction between the floor and the refrigerator is 0.30.Depending on where you push,the refrigerator may start to tip over before it starts to slide along the floor.What is the highest distance above the floor that you can push the refrigerator so that it will not tip before it begins to slide?

A 3.00-m-long 200-N ladder,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 object is placed on the apparatus 2.0 m from one end,as shown in the figure.What are the forces,A and B,that the two wires exert on the beam?

A 95-N force exerted at the end of a 0.32-m long torque wrench produces a torque of 15 N ∙ m.What is the angle (less than 90°)between the wrench handle and the direction of the exerted force?

In the figure,a uniform 200-N ladder 10 m in length leans against a perfectly smooth wall.A 600-N firefighter climbs a distance x up the ladder.The coefficient of static friction between the ladder and the floor is 0.50.What is the maximum value of x for which the ladder will not slip?

Consider the sun and its largest planet Jupiter.On the line joining them,how far from the center of the sun is their center mass? Is it within or outside the sun? (Jupiter-sun distance is 778 × 10⁶ km,diameter of the sun is 1.4 × 10⁶ km,the sun is 1000 times as massive as Jupiter)

The figure shows a person's foot.In that figure,the Achilles tendon exerts a force of magnitude F = 720 N.What is the magnitude of the torque that this force produces about the ankle joint?

A 30-kg child stands at one end of a floating 20-kg canoe that is 5.0-m long and initially at rest in the water.The child then slowly walks to the other end of the canoe.How far does the canoe move in the water,assuming water friction is negligible?

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?

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.What magnitude forces do the sawhorses exert on the board?

The center of mass of a two-particle system is at the origin.One particle is located at (3.0 m,0.0 m)and has a mass of 2.0 kg.The other particle has a mass of 3.0 kg.What is the location of the 3.0-kg particle?

A man in a gym is holding an 8.0-kg object at arm's length,a distance of 0.55 m from his shoulder joint.What is the torque about his shoulder joint due to the object if his arm is horizontal?

A 1.0-g bead is at (-2.0 cm,2.0 cm),a 2.0-g bead is at (2.0 cm,-4.0 cm),and a 3.0-g bead is at (2.0 cm,0.0 cm).What are the coordinates of the center of mass of this system of beads?

A man in a gym is holding an 8.0-kg object at arm's length,a distance of 0.55 m from his shoulder joint.What is the torque about his shoulder joint due to the object if his arm is held at 30° below the horizontal?

Five forces are exerted on a rod that is free to pivot at point P,as shown in the figure.Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice.)

In the figure,four point objects are placed as shown.Assume that all the numbers in the figure are accurate to two significant figures.What are the x and y coordinates of the center of mass of this arrangement?

A force of 17 N is exerted to the end of a 0.63-m long torque wrench at an angle 45° from a line joining the pivot point to the handle.What is the magnitude of the torque about the pivot point produced by this force?

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?