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# Equilibrium

### Vertical Mass-and-Spring Oscillator

A block of mass is attached to the end of an ideal spring. Due to the weight of the block, the block remains at rest when the spring is stretched a distance from its equilibrium length. The spring has an unknown spring constant. A. What is the spring constant? B. Suppose that the block gets bumped and undergoes a small verti

### Harmonic Oscillator Kinematics

One end of a spring with spring constant k is attached to the wall. The other end is attached to a block of mass m. The block rests on a frictionless horizontal surface. The equilibrium position of the left side of the block is defined to be x=0. The length of the relaxed spring is L... (see attached) Please do not place your

### Physics (solving for optimal diameter of rope to support given weight)

An artist friend of yours needs help hanging a 500 lb sculpture from the ceiling. For artistic reasons, she wants to use just two ropes. One will be 30 degrees from vertical, the other 60 degrees. She needs you to determine the smallest diameter rope that can safely support this expensive piece of art. On a visit to the hardware

### Submerged Block

A beaker contains a thick layer of oil floating on water. A cubical block of wood is gently lowered into the beaker, so as not to disturb the layers of liquid, until it floats peacefully between the layers, as shown. a) What is the distance between the top of the wood cube (after it has come to rest) and the interface between

### Walking the Plank

Please do not place your response in a .pdf format, but Word documents are okay. Thanks! A horizontal uniform bar of mass m and length L is hung horizontally on two vertical strings. String 1 is attached to the end of the bar and string 2 is attached a distance L/4 from the other end. A monkey of mass m/2 walks from one end o

### Translational Equilibrium

A leg and cast weighs 220 N (w1) The leg held in traction by two weights (w2 and w3) attached to strings and applies in order that there be no force exerted on the hip joint J by the leg in the cast. (In other words the leg is in translational equilibrium) what are the numerical values of w2 and a for this to happen if w3=110 N?

### Rope hanging between two trees - find the tension

A uniform rope of weigh W hangs between two trees; The ends of the rope are the same height, and they each make angle teta with the trees Find the tension at either end of the rope. Find the tension in the middle of the rope.

### Vector polygon to solve for the forces on a block in equilibrium on a plane.

A block whose weight is W= 250 nt is on a frictionless plane which is at angle q= 25 degrees. A cable between the ceiling and the block makes an angle q=55 degrees from the ceiling. See ATTACHMENT1 for a diagram with given parameters, angles, physics statements, and a polygon created from known information. Also an illustration

### Equilibrium Condition Functions

A container is partitioned by a porous, fixed, wall. Because the wall is porous, it allows particles to diffusive from one side to the other (note that by 'diffuse' I mean that there are tiny holes in the wall which allow the gas particles to make it through; there is not some big gaping hole). The wall also allows the flow of

### Speed of Blocks on an Incline

A block, mass = m1, lies on an incline of angle theta, and is connected to a second block of mass m2=3/2 m by a string that passes over a light frictionless pulley. The second block hangs vertically and is firmly attached to a spring that has negligible mass and a force constant of k. The opposite end of the spring is firmly a

### Equilibrium and Center of Mass

In Fig. 13-11, a horizontal scaffold, of length 2.00 m and uniform mass 50 kg, is suspended from a building by two cables. It has dozens of paint cans stacked on it at various points. The total mass of the paint cans is 77.0 kg. The tension in the cable at the right is 735 N. How far horizontally from that cable is the center of

### Finding Tension and Horizontal and Vertical Components of Force

The system in Fig. 13-37 is in equilibrium. A concrete block of mass m = 236 kg hangs from the end of the uniform strut whose mass is 46.5 kg. (Please see attachment). (a) Find the tension T in the cable. (b) Find the horizontal component of the force exerted on the strut by the hinge. (c) Find the vertical component of the

### Equilibrium/torque

Hi. I need some help with a conceptual question. "A uniform 1-meter stick that is supported by a fulcrum at the 25-cm mark is in equilibrium when a 1-kg rock is suspended at the 0 cm end. Is the mass of the meter stick greater than, equal to, or less than the mass of the rock?" I thought the answer would be that the mass o

### Finding the Density of a Block and Oil

A block of wood floats in fresh water with forty percent of its volume submerged. This block floats in oil with 93 percent of its volume submerged. (a) Find Db, the density of the block. (b) Find Do, the density of the oil.

### Torques on a boom in equilibrium.

A uniform boom is at an angle of 45 degrees from the ground. It is held in place by a frictionless pin at ground level. Weight A= 2230 nt is suspended from its upper end and the boom's weight B= 441 nt. A cable from its upper end to ground level makes angle 30 degrees with the ground. See ATTACHMENT for a diagram. Find T, the t

### A door in equilibrium requiring application of net torque equal to zero.

A uniform, rectangular door 2.2 m high and 2.4 m wide having a weight of 260 nt is supported by two hinges. One hinge is .30 m from the top corner and the other is .30 m from the bottom corner. Each hinge supports half the total weight of the door. See door ATTACHMENT for a diagram. Find the magnitude of the total force exert

### Spring supporting two blocks without friction

A 0.7 lb block rests on top of a 0.5 lb block supported by but not attached to a spring of constant 9 lb/ft. The upper block is sudenly removed. A) Determine the maximum velocity reached by the 0.5 lb mass B) the maximum height reached by the 0.5 lb mass Please see attachment

### Machines and Mechanics

1. A 0.100 kg meterstick is supported at its 40.0 cm mark by a string attached to the ceiling. A 0.700 kg mass hangs vertically from the 5.00 cm mark. A mass is attached somewhere on the meterstick to keep it horizontal and in both rotational and translational equilibrium. If the force applied by the string attaching the meterst

### A 0.100 kg meter-stick is supported at its 40.0 cm mark by a string attached to the ceiling.

1. A person lifts a 950 N box by pushing it up an incline. If the person exerts a force of 350 N along the incline, what is the mechanical advantage of the incline? 2. A 0.100 kg meter-stick is supported at its 40.0 cm mark by a string attached to the ceiling. A 0.700 kg mass hangs vertically from the 5.00 cm mark. A mass

### Rotational equilibrium

I am trying to help my brother (in high school) understand how to solve rotational equilibrium problems. What he needs is an explanation on how to approach these problems. I understand each problem is different, but I imagine there must be a general method for solving them. I have put a problem below so that hopefully you could

### Rigid Objects in Equilibrium, Center of Gravity

A lunch tray is being held in one hand. The mass of the tray itself is 0.200 kg, and its center of gravity is located at its geometrical center. On the tray is a 1.00-kg plate of food and a 0.250-kg cup of coffee. Obtain the force T exerted by the thumb and the force F exerted by the four fingers, Both forces act perpendicular t

### Tension - Equilibrium and Elasticity: Five problems

The graphs are attached in word document. 1. The system in the picture is in equilibruim with the string in the center exactly horizontal. Find (a) tension T 1 , (b) tension T 2 (c) tension T 3 (d) angel pheta 2. The system in the picture is in equilibrium. A concrete block of mass 225 kg hanfs from the end of the unif

### Simple harmonic motion of a mass on a spring

On a frictionless table, a spring whose force constant is 60 nt/m has one end fixed and the other attached to mass M= 3.9 kg. A cord connects mass M to a suspended rock whose mass is m= 3.2 kg. Assume an x axis origin at the movable end of the spring when the spring contains no potential energy. At some instant, with the system

### Fluid Mechanics: bouyance, harmonic motion, period

Consider an object with height h, mass M, and uniform cross sectional area A floating upright in a liquid with density p. a.) Calculate the vertical distance from the surface of the liquid to the bottom of the floating object at equilibrium. b.) A downward force of magnitude F is applied to the top of the object. At the

### Torque and static equilibrium of a uniform metal rod: find tension, force exerted

A uniform metal rod, with a mass of 3.1 kg and a length of 1.2m, is attached to a wall by a hinge at its base. A horizontal wire bolted to the wall 0.51 m above the base of the rod holds the rod at an angle of 25 degrees above the horizontal. The wire is attached to the top of the rod. (a) Find the tension in the wire.

### Equilibrium of a Rigid Body

One end of a post weighing 500N and with height h rests on a rough horizontal surface coefficient of static friction equal to .40. The upper end is held by a rope fastened to the surface and making an angle of 37 degrees with the post (see attached figure). A horizontal force F is exerted on the post as show in the attached diag

### Coefficient of friction: smallest value to maintain mass in an equilibrium position?

See attached graph. A cylinder of mass M and radius R rests on an inclined plane. It is held in place by a horizontal string that is attached to the edge of the cylinder. If the angle that the plane makes with the horizontal is theta, and the coefficient of static friction between the cylinder and the plane is u, what is the

### Speed of object in revolutions around a circle: puck of mass tied to a string

A puck of mass 0.270 kg is tied to a string and allowed to revolve in a circle of radius 1.09 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of 1.24 kg is tied to it (see figure in attached Word file). The suspended mass remains in equilibrium while

### Calculate tension in a steel wire under water connecting a buoy to the sea bed

A spherical buoy is tied to the sea bed by a steel wire so that exactly half the buoy is above the water surface. If the diameter of the buoy is 1.3m and the mass of the buoy is 20kg: a) determine the tension in the wire b) if this tension produces an extension in the steel wire of 4.0mm, calculate the length of the wire.

### Write equation of motion (Newton's Law) modeling a pendulum; find equilibrium points

A pendulum is modeled by a mass m, attached to one end of a light rod of lenght l, whose other end is attached to an axis. Write down the equation of motion (Newton's Law) modeling the pendulum. Rewrite the model as a system of two first order equations for the position and velocity of the mass. Find the equilibrium points an