A homeowner is trying to move a stubborn rock from his yard. By using a a metal rod as a lever arm and a fulcrum (or pivot point) the homeowner will have a better chance of moving the rock. The homeowner places the fulcrum a distance d = 0.200 m from the rock, which has a mass of 525 kg, and fits one end of the rod under the rock's center of weight. If the homeowner can apply a maximum force of 711 N at the other end of the rod, what is the minimum total length L of the rod required to moveſthe rock? Assume that the rod is massless and nearly horizontal so that the weight of the rock and homeowner's force are both essentially vertical. The acceleration due to gravity is g = 9.81 m/s². m L =

Chapter 12, Problem 037 GO In the figure, a uniform plank, with a length L of 6.83 m and a weight of 386 N, rests on the ground and against a frictionless roller at the top of a wall of height h = 2.78 m. The plank remains in equilibrium for any value of e = 70.0° or more, but slips if e < 70.0°. Find the coefficient of static friction between the plank and the ground. Roller Number Units the tolerance is +/-2% Click if you would like to Show Work for this question: Open Show Work

A ladder leans against a wall 5 meters above the ground so a homeowner can clear his gutters of leaves from last fall. The bottom of the ladder just begins to slip when it is 7.1 meters from the wall.  What is the coefficient of static friction between the bottom of the ladder and the ground?

An object can rotate but not exhibit no angular acceleration and no linear or translational acceleration. Such an object is in both translational and rotational equilibrium. What are the conditions for the object to be in static equilibrium? A vaulter holds a 29.4 -N pole in equilibrium by exerting an upward force U with her leading hand and a downward force D with her trailing hand as shown. Point C is the center of gravity of the pole where the 29.4 N acts. Determine: The magnitude of U The magnitude of D

A uniform ladder 5.0 m long rests against a frictionless, vertical wall with its lower end 3.0 m from the wall. The ladder weighs 140 N. A man weighing 620 N climbs slowly up the ladder. Start by drawing a free-body diagram of the ladder. What is the actual frictional force when the man has climbed 1.0 m along the ladder? [Hint: Draw a free body diagram to determine what forces are at play. Then use the torque formula (T = Fxrx sine) to find the net torque.]

A 2.00-m-long, 500 kg steel uniform beam extends horizontally from the point where it has been bolted to the framework of a new building under construction. A 70 kg construction worker stands at the far end of the beam. What is the magnitude of the torque about the bolt due to the worker and the weight of the beam?

A hungry bear weighing 700 N walks out on a beam in an attempt to retrieve a basket of goodies hanging at the end of the beam (Fig. P8.22). The beam is uniform, weighs 200 N, and is 6.00 m long, and it is supported by a wire at an angle of 0 = 60.0°. The basket weighs 80.0 N. (a) Draw a force diagram for the beam. (b) When the bear is at x = 1.00 m, find the tension in the wire supporting the beam and the components of the force exerted by the wall on the left end of the beam. (c) If the wire can withstand a maximum tension of 900 N, what is the maximum distance the bear can walk before the wire breaks?

When a gymnast weighing 740 N executes the iron cross as in figure (a), the primary muscles involved in supporting this position are the latissimus dorsi ("lats") and the pectoralis major ("pecs"). The rings exert an upward force on the arms and support the weight of the gymnast. The force exerted by the shoulder joint on the arm is labeled F while the two muscles exert a total force F on the arm. Determine the magnitude of the force F Note that one ring supports half the weight of the gymnast, which is w 370 N as indicated in figure (b). Assume that the force F acts at an angle of 45° below the horizontal at a distance of 4.0 cm from the shoulder joint. In your estimate, take the distance from the shoulder joint to the hand to be L = 75 cm and ignore the weight of the arm. m kN Shoulder joint 4.0 cm- 45.00 Ed Bock/CORBIS

You have been hired to design a family-friendly see-saw. Your design will feature a uniform board (mass M = 11 kg, length L = 11 m) that can be moved so that the pivot is a distance d from the center of the board. This will allow riders to achieve static equilibrium even if they are of different mass, as most people are. You have decided that each rider will be positioned so that his/her center of mass will be a distance xoffset = 29 cm from the end of the board when seated as shown.You have selected a child of mass m = 23 kg (shown on the right), and an adult of mass n =3 times the mass of the child (shown on the left) to test out your prototype. 1) Determine the distance d in m. d = 2) Determine the magnitude of the force exerted on the pivot point by the see-saw in N. Fb =

Fy Ex The plant in the picture has mass of 30 kg, and is hanging at a distance of 1.8 meters from the wall. The horizontal rod has mass of 7.8 kg. Assume that its weight is evenly distributed, therefore it can be treated as a single force at the center of mass. The rod is 2 meters long, and there is a cable at a 38° angle supporting it at the end. Using the wall as the axis of rotation, find the magnitude of the downward torque, from both the weight of the rod and the weight of the plant.