finding and using the Center of gravity




We can often use symmetry considerations to locate the center of gravity of a body, just as we did for the center of mass. The center of gravity of a homoge-neous sphere, cube, or rectangular plate is at its geometric center. The center of gravity of a right circular cylinder or cone is on its axis of symmetry.

For a body with a more complex shape, we can sometimes locate the center of gravity by thinking of the body as being made of symmetrical pieces. For example, we could approximate the human body as a collection of solid cylinders, with a sphere for the head. Then we can locate the center of gravity of the combination with Eqs. (11.3), letting m1, m2, c be the masses of the individual pieces and 1x1, y1, z12, 1x2, y2, z22, c be the coordinates of their centers of gravity.

When a body in rotational equilibrium and acted on by gravity is supported or suspended at a single point, the center of gravity is always at or directly above or below the point of suspension. If it were anywhere else, the weight would have a torque with respect to the point of suspension, and the body could not be in rotational equilibrium. Figure 11.4 shows an application of this idea.

finding and using the Center of gravity

Topics You May Be Interested In
Conditions For Equilibrium The Continuity Equation
Gases Liquid And Density Bernoulli's Equation
Pressure, Depth, And Pascals Law Kepler's First Law
Pascal Law Spherical Mass Distributions
Surface Tension A Visit To A Black Hole

 

 

 

 

Topics You May Be Interested In
Solving Physics Problems Pressure In A Fluid
Conditions For Equilibrium Absolute Pressure And Gauge Pressure
Finding And Using The Center Of Gravity Gravitation
Summary Of Equilibrium And Elasticity Satellites: Circular Orbits
Gases Liquid And Density Apparent Weight And The Earth’s Rotation

 

 

 

 

Topics You May Be Interested In
Using And Converting Units Solved Problems
Uncertainty And Significant Figures Gravitation
Center Of Gravity Satellites: Circular Orbits
Summary Of Equilibrium And Elasticity Describing Oscillation
Deriving Bernoullis Equation Simple Harmonic Motion

 

 

 

 

Topics You May Be Interested In
Solving Physics Problems The Motion Of Satellites
Standards And Units Kepler's Second Law
Finding And Using The Center Of Gravity Black Holes
Bulk Stress And Strain A Visit To A Black Hole
Gravitation Simple Harmonic Motion

 

 

 

 

Topics You May Be Interested In
Standards And Units Absolute Pressure And Gauge Pressure
Using And Converting Units More On Gravitational Potential Energy
Uncertainty And Significant Figures Black Holes
Center Of Gravity Circular Motion And The Equations Of Shm
Bulk Stress And Strain Period And Amplitude In Shm

 

 

 

 

Topics You May Be Interested In
Uncertainty And Significant Figures Examples On Gravition
Solving Rigid-body Equilibrium Problems The Motion Of Satellites
Tensile And Compressive Stress And Strain Kepler's Second Law
Deriving Bernoullis Equation Detecting Black Holes
Determining The Value Of G Amplitude, Period, Frequency, And Angular Frequency

Using the same reasoning, we can see that a body supported at several points must have its center of gravity somewhere within the area bounded by the supports. This explains why a car can drive on a straight but slanted road if the slant angle is relatively small (Fig. 11.5a) but will tip over if the angle is too steep (Fig. 11.5b). The truck in Fig. 11.5c has a higher center of gravity than the car and will tip over on a shallower incline.

finding and using the Center of gravity

 

 

Topics You May Be Interested In
Nature Of Physics Examples On Gravition
Bulk Stress And Strain Spherical Mass Distributions
Elasticity And Plasticity A Point Mass Inside A Spherical Shell
Fluid Mechanics Apparent Weight And The Earth’s Rotation
Buoyancy Describing Oscillation

The lower the center of gravity and the larger the area of support, the harder it is to overturn a body. Four-legged animals such as deer and horses have a large area of support bounded by their legs; hence they are naturally stable and need only small feet or hooves. Animals that walk on two legs, such as humans and birds, need relatively large feet to give them a reasonable area of support. If a two-legged animal holds its body approximately horizontal, like a chicken or the dinosaur Tyrannosaurus rex, it must perform a balancing act as it walks to keep its center of gravity over the foot that is on the ground. A chicken does this by moving its head; T. rex probably did it by moving its massive tail.



Frequently Asked Questions

+
Ans: In most equilibrium problems, one of the forces acting on the body is its weight. We need to be able to calculate the torque of this force. The weight doesn’t act at a single point; it is distributed over the entire body. But we can always calculate the torque due to the body’s weight by assuming that the entire force of gravity (weight) is concentrated at a point called the center of gravity view more..
+
Ans: In this chapter we’ll apply the first and second conditions for equilibrium to situations in which a rigid body is at rest (no translation or rotation). Such a body is said to be in static equilibrium view more..
+
Ans: A body that can be modeled as a particle is in equilibrium whenever the vector sum of the forces acting on it is zero. But for the situations we’ve just described, that condition isn’t enough. If forces act at different points on an extended body, an additional requirement must be satisfied to ensure that the body has no tendency to rotate: The sum of the torques about any point must be zero. This requirement is based on the principles of rotational dynamics view more..
+
Ans: We can often use symmetry considerations to locate the center of gravity of a body, just as we did for the center of mass. The center of gravity of a homoge-neous sphere, cube, or rectangular plate is at its geometric center. The center of gravity of a right circular cylinder or cone is on its axis of symmetry. view more..
+
Ans: There are just two key conditions for rigid-body equilibrium: The vector sum of the forces on the body must be zero, and the sum of the torques about any point must be zero. To keep things simple, we’ll restrict our attention to situations in which we can treat all forces as acting in a single plane, which we’ll call the xy-plane view more..
+
Ans: Here are some solved examples to help your concepts to be more clear. view more..
+
Ans: The rigid body is a useful idealized model, but the stretching, squeezing, and twisting of real bodies when forces are applied are often too important to ignore. view more..
+
Ans: The simplest elastic behavior to understand is the stretching of a bar, rod, or wire when its ends are pulled (Fig. 11.12a). Figure 11.14 shows an object that initially has uniform cross-sectional area A and length l0. We then apply forces of equal magnitude F# but opposite directions at the ends (this ensures that the object has no tendency to move left or right). We say that the object is in tension. view more..
+
Ans: When a scuba diver plunges deep into the ocean, the water exerts nearly uniform pressure everywhere on his surface and squeezes him to a slightly smaller volume. This is a different situation from the tensile and compressive stresses and strains we have discussed. view more..
+
Ans: The third kind of stress-strain situation is called shear. The ribbon in Fig. 11.12c is under shear stress: One part of the ribbon is being pushed up while an adjacent part is being pushed down, producing a deformation of the ribbon. view more..
+
Ans: Hooke’s law—the proportionality of stress and strain in elastic deformations— has a limited range of validity. In the preceding section we used phrases such as “if the forces are small enough that Hooke’s law is obeyed.” Just what are the limitations of Hooke’s law? What’s more, if you pull, squeeze, or twist anything hard enough, it will bend or break view more..
+
Ans: summary of equilibrium and elasticity view more..
+
Ans: Fluids play a vital role in many aspects of everyday life. We drink them, breathe them, swim in them. They circulate through our bodies and control our weather. The physics of fluids is therefore crucial to our understanding of both nature and technology view more..
+
Ans: A fluid is any substance that can flow and change the shape of the volume that it occupies. (By contrast, a solid tends to maintain its shape.) We use the term “fluid” for both gases and liquids. The key difference between them is that a liquid has cohesion, while a gas does not. The molecules in a liquid are close to one another, so they can exert attractive forces on each other and thus tend to stay together (that is, to cohere). That’s why a quantity of liquid maintains the same volume as it flows: If you pour 500 mL of water into a pan, the water will still occupy a volume of 500 mL. The molecules of a gas, by contrast, are separated on average by distances far larger than the size of a molecule. Hence the forces between molecules are weak, there is little or no cohesion, and a gas can easily change in volume. If you open the valve on a tank of compressed oxygen that has a volume of 500 mL, the oxygen will expand to a far greater volume. view more..
+
Ans: A fluid exerts a force perpendicular to any surface in contact with it, such as a container wall or a body immersed in the fluid. This is the force that you feel pressing on your legs when you dangle them in a swimming pool. Even when a fluid as a whole is at rest, the molecules that make up the fluid are in motion; the force exerted by the fluid is due to molecules colliding with their surroundings view more..
+
Ans: If the weight of the fluid can be ignored, the pressure in a fluid is the same throughout its volume. We used that approximation in our discussion of bulk stress and strain in Section 11.4. But often the fluid’s weight is not negligible, and pressure variations are important. Atmospheric pressure is less at high altitude than at sea level, which is why airliner cabins have to be pressurized. When you dive into deep water, you can feel the increased pressure on your ears. view more..
+
Ans: Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. view more..
+
Ans: If the pressure inside a car tire is equal to atmospheric pressure, the tire is flat. The pressure has to be greater than atmospheric to support the car, so the significant quantity is the difference between the inside and outside pressures. When we say that the pressure in a car tire is “32 pounds” (actually 32 lb>in.2 , equal to 220 kPa or 2.2 * 105 Pa), we mean that it is greater than atmospheric pressure (14.7 lb>in.2 or 1.01 * 105 Pa) by this amount. view more..




Rating - 4/5
548 views

Advertisements