A beam resting on two pivots has a length of L = 6.00 m and mass M = 77.0 kg. The pivot under the left end exerts a normal force n₁ on the beam, and the second pivot placed a distance = 4.00 m from the left end exerts a normal force n₂. A woman of mass m = 61.0 kg steps onto the left end of the beam and begins walking to the right as in the figure below. The goal is to find the woman's position when the beam begins to tip. m M (a) Sketch a free-body diagram, labeling the gravitational and normal forces acting on the beam and placing the woman x meters to the right of the first pivot, which is the origin. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet. (b) Where is the woman when the normal force n₁ is the greatest? x = m (c) What is n, when the beam is about to tip? N

A board of mass 3.0Kg serves as a seesaw for two children. Child A has a mass of 40Kg and sits 2.5m from the pivot point. At what distance x should a child B of mass 25Kg sit from the pivot point so as to balance the seesaw? What is the normal force at the pivot point? Assume the board is uniform and centered over the pivot.

A rod is laying on top on two poles. The rod is uniform and has a length of 3.22 m. The left pole is at the left end of the rod and the right pole is a 0.41m (d-0.41m) from the right side of the rod. What is the ratio of the forces F/FR on the rod due to the two poles?

A 16.0-m uniform ladder weighing 510 N rests against a frictionless wall. The ladder makes a 57.0° angle with the horizontal. (a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when an 850-N firefighter has climbed 3.90 m along the ladder from the bottom. Horizontal force: magnitude direction Vertical force: magnitude direction towards the wall up N ✓✓ N (b) If the ladder is just on the verge of slipping when the firefighter is 8.70 m from the bottom, what is the coefficient of static friction between ladder and ground?

A diver of weight 580 N stands at the end of a diving board of length L= 4.3 m and negligible mass (see the figure below). The board is fixed to two pedestals separated by distance d = 1.3 m. Take the upward direction to be positive. Of the forces acting on the board, what are (a) the force from the left pedestal and (b) the force from the right pedestal? (a) Number (b) Number 368.9 948.9 Units Units TOENE N N

A 740 N bear is standing on a metal plank supported by the cable shown in the figure. At the end of the plank hangs a basket weighing 80 N. Assume the plank is uniform, weighs 200 N, is 5.50 m long, and 0 = 60.0°. Goodies (a) When the bear is at x = 1.10 m, find the tension in the cable supporting the plank and the components of the force exerted by the wall on the left end of the plank. (Enter the magnitudes of your answers in N.) T = F = F = N N N (b) If the cable can withstand a maximum tension of 875 N, what is the maximum distance (in m) the bear can walk before the cable breaks? (Measure this distance from the wall.) m

Question 4. A rod is lying on the top of a table. One end of the rod is hinged to the table so that the rod can rotate freely on the table top. Two forces, both parallel to the table top, act on the rod at the same place. One force is directed perpendicular to the rod and has a magnitude of 31 N. The second force has a magnitude of 52 N and is directed at an angle with respect to the rod. If the sum of the torques due to the two forces is zero, what must be the angle? Ans: 36.59°

A diver of weight 510 N stands at the end of a diving board of length L = 4.9 m and negligible mass (the figure). The board is fixed to two pedestals separated by distance d = 2.0 m. Take the upward direction to be positive. Of the forces acting on the board, what are (a) the force from the left pedestal and (b) the force from the right pedestal? L (a) Number Units (b) Number Units

There is this ladder with a length L = 3.5 m and mass M= 15 kg leans against a smooth vertical wall, while its bottom legs rest on a rough horizontal floor. There is also static friction between floor and ladder is u = 0.47. The ladder makes an angle 0 = 55° with respect to the floor. A person of mass 8M stands on the ladder a distance d from its base. What is the magnitude of the normal force N, in newtons, exerted by the floor on the ladder? What is the largest distance up the ladder dmax, in meters, that the person can stand without the ladder slipping?

A gymnast with mass 55.0 kg stands on the end of a uniform balance beam as shown in the figure below. The beam is 5.00 m long and has a mass of 250 kg (excluding the mass of the two supports). Each support is 0.700 m from its end of the beam. In unit-vector notation, what are the forces on the beam due to support 1 and support 2? L. (a) F1 = N (b) F2 = N