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
A 10kg aluminum block of (c=920J/KgC) at 75 degrees C is dropped into 100kg of water ( c=4186J/kgC) at 50 degrees C. Assuming the heat only passes between the water and the aluminum (no losses) what will the equilibrium temperature (in degrees C) be?
8 grams of water at 100 degrees C are poured into a cavity at 0 degrees C. How many g of ice melt before thermal equilibrium is attained?
A uniform plank with a length L of 6.10 m and a weight of 445 N, rests on the ground and against a frictionless roller at the top of the wall of height h = 3.05 m. The plank remains in equilibrium for any value of theta greater than or equal to 70 degress but slips if theta is less than 70 degrees. Find the coefficient of stat
What magnitude of force applied horizontally at the axle of the wheel is necessary to raise the wheel over an obstacle of height h? The wheel's radius is r and its mass is m. The wheel is shown on a flat surface resting against a step of height h. The point touching the step is at 4 o'clock on the wheel.
See attachment #1 for diagram. Using Archimedes' principle and equilibrium of two submerged objects to find unknown density. Find he density of an irregularly shaped plastic object found floating in the sea. Its mass is Mp= 1.25 kg. It is tied by a cord to a block of aluminum, mass Ma= 1.5 kg, whose density is Da= 2700 kg
Here is the asking problem: A cord is attached to and partially wound around a cylinder of weight W and radius r which rests on an incline as shown. Knowing that the coefficient of static friction between the cylinder and the incline is 0.30, find the smallest allowable value of angle if the cylinder is to remain in equilibri
A scaffold of mass 35 kg and length 5.8 m is supported in a horizontal position by one vertical cable at each end. A window washer of mass 86 kg stands at a distance d from the midpoint of the scaffold. The tension in the cable nearest the worker is twice the tension in the other. a) What is the tension in the cable nearest th
The system in figure 13-45 is in equilibrium. A mass of 225 kg hangs from the end of the uniform strut. The tension T in the supporting cable is measured to be 6,910 N. a) What is the mass of the strut? b) What is the vertical component of the force exerted on the strut by the hinge? c) What is the horizontal component of th
If a mass of 600.0 g is hung from the bottom of a vertical spring, the spring will stretch 28.0 cm. Now the hanging mass is removed, and the spring is placed horizontally on a frictionless table. One end of the spring is held fixed and the other end is attached to a 370.0 g mass. The mass is then pulled out a distance of 14.0 cm
A unifom cylinder, mass M= 15 kg, rests on a plane inclined at angle b=30°, held stationary by a cord attached to the plane at angle a= 50° which applies tangential force C to the cylinder. A mass m= 5 kg is suspended on a cable which is wrapped on the surface of the cyiinder. The radius R is unknown. See the attachment for a
Determine when a solid shape produced by gluing a cylinder of height H and radius R to a hemisphere of radius R made from the same material will be in a stable equilibrium standing on its top.
Two masses are at rest on a plane inclined at angle s=35° above horizontal. A cord from mass A=4 kg, passes over a frictionless pulley at the top of the plane to unknown mass B. The coefficient of friction is f= .25. See attachment for picture showing blocks and plane. a. Find the maximum mass of B for the masses to remain i
Five solid objects made of different materials are placed in a tub of water. The objects are cubes made of wood, ice, aluminum, steel and gold. All of the objects have the SAME mass. The objects are released and allowed to reach some equilibrium position. Note that some of the objects will float, while others will sink. Whic
The asking problem: The uniform rod AB lies in a vertical plane. Its ends are connected to rollers which rest against frictionless surfaces. Determine the relation between the angles teta and alpha when the rod is in equilibrium. Note: This is a 2D problem and not a 3D. It was taken from the «Statics of Rigid Bodies in Two Di
The eight figures show various situations where blocks of different weights are attached by ropes to rigidly fixed objects or to other blocks, which are attached to fixed objects. The situations differ in a number of ways, as the figures show, but all situations represent static equilibrium (i.e. nothing is moving). The weights
The sailor in Figure P8.10 weighs 750N. The force F1 exerted by the wind on the sail is horizontal and acts through point B. The weight of the boat is 1250N and acts through point O, which is 0.8m from the point A along the line OA. The force F2 exerted by the water acts through point A. Determine the net force exerted by t
Explain the important laws of thermodynamics and their physical aspects.
Three equal charges, Q coulombs are located at the vertices of a triangle as shown in the figure. The charges are connected together by strings as shown in the figure. If the length of each string is L, determine the tension in the strings.
There is a 200lb wieght on a table. attached to the mass is a string with the other end attached to a wall. hanging from the string is another string with the other end of that string attached to a unknow wieght. the string between the 200 lb mass and the wall form the following angles: from wall 70 degrees South West, and from
A surveillance TV camera is hung from the roof by 2 cables. If the tension on the left cable is T2=12N, find T1 and the weight of the camera. The angle between T2 and the roof is 20 deg and the angle between T1 and roof is 30 degrees.