Exam 11: Static Equilibrium

Three children acrobats are standing still on a circular horizontal platform of radius 4 m suspended at the center.The origin of the xy - Cartesian coordinate system is in the center of the circular platform.A 30-kg child is located at (1 m,2 m),and a 40-kg child is located at (-1 m,- 2 m).Assuming the children stand still on their positions,where must a 20-kg child acrobat be located so that the center of mass of the system consisting of the three children is at the origin and the platform is balanced?

A ladder of uniform density,length L and weight W rests on a rough floor (µ_s = 0.45)and against a frictionless wall.The maximum value of the angle between the wall and the ladder to prevent slipping is

Your friend Joe hangs from a horizontal bar by his two hands,with his arms each inclined 35 degrees from the vertical (so that his arms have an angle between them of 70 degrees.If his mass is 76 kg,what is the tension in each of his arms?

Your precocious,22-kg,six year old sister sits on a swing and asks you to give her an amplitude of 32 degrees for her swing path.In order to do this precisely,you pull her back so that the angle with the vertical that the swing chains make is 32 degrees,and then you let go.As you held her at 32 degrees,what horizontal force were you applying to her?

A construction supervisor of mass M = 80.0 kg is standing on a board of mass m = 30.0 kg.Two sawhorses at a distance L = 4.00 m apart support the board.If the man stands a distance x₁ = 1.25 m away from sawhorse 1 as shown,what is the force that the board exerts on the other sawhorse?

A 5.0-m long uniform ladder leans against a smooth wall and its base rests on a rough floor.The ladder has a mass of 18.0 kg and its base is a distance of 2.3 m from the wall.If the ladder is to remain in place,what frictional force must be exerted by the floor on the ladder?

An object is in static equilibrium.It's then moved a short distance to the right and released.If the equilibrium is unstable,then what will happen next?

A board,with a weight of 85 N and a length of 6.0 m,is supported by two vertical ropes,as shown in the figure.Rope A is connected to one end of the board and rope B is connected a distance of 1.5 m from the other end of the board.A box with a weight of 25 N is placed on the board with its center of mass 1.0 m from rope A. What is the tension in rope B on the right?

A diving board is 2.20 m long,has a mass of 5.20 kg and has a uniform density.There are supports holding it in place at one end (F1)and another 25.0 cm from the same end (F2).Find the support each of the support provides.Take upward forces to be positive.

A flat,horizontal uniform plank is supported underneath by a triangular wedge which itself rests on flat,level ground.An object that has the same weight as the plank is placed on the left end of the plank.Where must the wedge be placed under the plank in order for the system to be in equilibrium?

A track is built whose height as a function of horizontal position x is given by (h and x,both in meters).If a marble is placed on this track,find the position where it will be in a stable equilibrium.

During a picnic,you and two of your friends decided to have a three-way tug of war using three ropes tied in a knot in the middle.All of you pull with forces of the same magnitude,550 N.Alice pulls to the south and Bob pulls 30 ^$\circ$ north of east.What is the angular orientation of your rope so that the knot stays at rest?

A 25-kg 10-m ladder is leaning against a frictionless wall with its base making an angle of 32 ^$\circ$ to the horizontal.What is the magnitude of the force exerted on the ladder by the ground?

The distance between the front wheels and the back wheels of the professor's car is 4 m.The center of mass of the car is located 1 m from the front wheels.If the car has a mass of 1020 kg,what are the forces that the cars two front tires,F_f,and two rear tires,F_r,exert on the street,when the car is standing on a horizontal surface?

You wish to measure the strength of your biceps muscle by exerting a force on a test strap attached to a scale.When you pull on the strap,the scale moves and the movement measures the strength of your biceps.The strap is at 30 cm at the elbow and the biceps muscle is attached at a 5 cm from the pivot point.If the scale reads 20 N,the force exerted by the biceps muscle is

A 33-kg bowling ball is held up on a frictionless vertical wall by a string.The string goes from the bowling ball to an attachment point on the wall directly above the ball.The string makes an angle of 34 ^$\circ$ with respect to vertical.The horizontal force that the wall exerts on the ball is

The definition of neutral equilibrium of a system is

A 30-kg uniform ladder 12 m long is leaning against a frictionless wall at an angle of 50 degrees above the horizontal.A 45-kg boy climbs 5.0 m up the ladder.What is the magnitude of the force exerted by the ladder on the wall?

A 5.00-m long uniform ladder leans against a smooth wall and its base rests on a rough floor.The ladder has a mass of 18.0 kg and its base is a distance of 2.30 m from the wall.A person of mass 80.0 kg climbs 2.50 m up the ladder.If the ladder is to remain in place,what frictional force must be exerted by the floor on the ladder?

A pivot is placed under a massless 100-cm pole at 50 cm from the ends.A 4-kg mass is hung 15 cm from the left end and a 3-kg mass is hung 45 cm from the left end.If the stick is to remain in rotational equilibrium,how far from the left end of the pole must a third 8-kg mass have be hung?