F, m2 m, W2 w,

For two existing torques, what third force at a given distance from the pivot will balance them? Imagine a meter stick set up as in the figure. It hangs from a central bracket, and two hanging masses can hang from it from each of their brackets. At a third location, a force probe can either pull up or pull down on the stick, depending on what is needed to balance the stick. The mass of the meter stick is 120 g. sketch the situation (drawing r1, r2, r3, F1, F2, and F3) and determine the magnitude (value) and direction (+ or -) of each torque. Don't include the mass of a bracket that would hold the hanging mass in place; assume the mass listed is the entire mass hanging at that point. For each trial, use the principle of equilibrium (where the sum of torques is zero) to calculate the third, unknown force acting at x3

Computation A 6-kg bowling ball rests on a uniform beam of length L and mass M, as in the figure. The beam is supported at two points separated by a distance BL where ß = 0.59 and the bowling ball is a distance d from support point 1. Find the largest distance dmax such that the beam does not tip if M = 17 kg and L = 4.9 m. [Note: To keep the bowling ball on the beam, report an answer of dmax ≤ L. For some values, a correct calculation gives dmax > L. That means the bowling ball can be placed anywhere on the beam without tipping and, in that case, the correct answer is dmax = L = 4.9 m.) 2 dmax m L BL- d M Report your numerical answer below, assuming three significant figures. Remember to include a "-" as necessary. O Search 1

Two blocks, each of mass 2 kg are suspendedfrom the ends of a rigid massless rod of lengthL. The rod is held horizontally on the fulcrumand then released. The length L1 is 15 cm andthe length L2 is 85 cm. Draw the force diagram for the rod. Clearly label all forces. Write Newton’s 2nd Law equation: (for F of y) Write Newton’s 2nd Law equation: (for net torque) What is the magnitude of the linear acceleration of the block closest to the fulcrum? What is the magnitude of the linear acceleration of the block furthest from the fulcrum?

The uniform seesaw shown below is balanced on a fulcrum located d1 = 3.5m from the left end. The bigger boy on the left end has a mass m1 =75 kg. The smaller boy on the right end has a mass of m2 = 55 kg and is a distance d2 = 4.5 m from the fulcrum. The mass of the board is mb.    Draw all forces acting on the seesaw board showing their directions and locations. Where would you draw the weight of the board? Identify and show the direction of rotations caused by the torques provided by all forces about the fulcrum. If the seesaw is in static equilibrium, write down the two conditions of static equilibrium symbolically using the forces and distances in the figure. Solve for the mass of the board. Calculate the force of fulcrum on the board.

A 1 490-kg automobile has a wheel base (the distance between the axles) of 2.70 m. The automobile's center of mass is on the centerline at a point 1.05 m behind the front axle. Find the force exerted by the ground on each wheel. each front wheel _______kN each rear wheel _______kN

The diagram above shows a 3.00 m long uniform beam. The left end of the beam is attached to a wall by a frictionless pivot. The beam is supported by a string that keeps the beam horizontal. The string makes an angle of 35.0° relative to vertical. The beam has a mass of 7.00 kg. A 2.00 kg mass is located at the end of the beam. A 6.00 kg mass is located 1.00 m from the 2.00 kg mass, as shown in the diagram. a.  What is the tension in the string? b.  What is the y-component of force applied to the beam by the pivot?

For two existing torques, what third force at a given distance from the pivot will balance them? Imagine a meter stick set up as in the figure. It hangs from a central bracket, and two hanging masses can hang from it from each of their brackets. At a third location, a force probe can either pull up or pull down on the stick, depending on what is needed to balance the stick. The mass of the meter stick is 120 g. sketch the situation (drawing r1, r2, r3, F1, F2, and F3) and determine the magnitude (value) and direction (+ or -) of each torque. Don't include the mass of a bracket that would hold the hanging mass in place; assume the mass listed is the entire mass hanging at that point. For each trial, use the principle of equilibrium (where the sum of torques is zero) to calculate the third, unknown force acting at x3

The center of mass of the arm shown in the figure is at point A. Find the magnitudes (in N) of the tension force F and the force F which hold the arm in equilibrium. (Let 8 = 24.0°.) Assume the weight of the arm is 48.3 N. IF 8.00 cm 29.0 cm 1₂ 354 X Draw a diagram showing the forces and distances. Find the sum of the torques about point O, and set this equal to zero. Solve your equation for F₁. N 340.30 X Apply Newton's second law in the x and y directions, and solve for F Sx Pythagorean theorem to calculate F. . N and F You will need your value of F. Then use the sy'