Equilibrium and Center of Gravity

CENTER OF GRAVITY AND EQUILIBRIUM

If we look at giant structures like tall buildings, long bridges and large dams, we observe that they are strong and stable. Engineers and architects carefully planned these structure to make it rigid, strong and in equilibrium so that it will not collapse especially during earthquake. Objects wherein all parts remain at constant or fixed distances from every other parts as the object rotates are called rigid bodies. Rigid bodies do not bend or stretch when forces act on them. The concept of rigid bodies is an idealized model because in a natural world, somehow materials deformed.

EQUILIBRIUM

            Consider a book that lies above the table. What are the forces acting on the book? It is just the weight? If the only force acting on the book is the weight, the book will be on free fall. There could be another force that acts on the book resting on the table. There is a support force from the table and you call it the normal force.

            As shown in the figure, the table exerts a force upward equal to the weight of the book. The book is at rest and the net force is equal to zero. Therefore we could say that the book is in the state of equilibrium.

  

CENTER OF GRAVITY

Let us recall the definition of weight. We know that weight is the force in which the object is pulled by the earth. In the study of equilibrium, we should know where the force acts. In chemistry, you learned that matter is made up of tiny particles. Each of these particles has weight, Each particle is acted by the force of gravity. The sum of the weights of all particles that compose the matter maybe considered as concentrated in one point. This point is called the center of gravity.

STATES OF EQUILIBRIUM

            Any object at rest can be classified in their state of equilibrium. Being stable, unstable or neutral. The equilibrium condition is affected by the location of the center of gravity in the object. When the center of gravity of an object is at the lowest possible position, it is in stable equilibrium. When the center of gravity of an object is at the highest possible position, it is in unstable equilibrium. When the center of gravity is neither lowered nor raised when it is slightly disturbed, it is neutral. 

Projectile Motion

In kinematics, the motion of a particle in a straight line. We distinguished between uniform motion, such as a billiard ball moving horizontally in a constant velocity; and uniformly accelerated motion such as a mango falling vertically under the influence of gravity. Now we are going to consider objects moving in a nonlinear motion or in a curved path. When you kicked a soccer ball with a certain angle, it follows a curved path. The path is known as a trajectory. The curved path motion is a combination of a uniform horizontal motion and a uniformly accelerated vertical motion.  Take note that the velocity of the kicked ball at any instant has two components of motion. The horizontal motion does not affect the vertical motion. This motion is called projectile motion.

We are fond of playing or watching a volleyball, football or a basketball match. The ball thrown or kicked in air is an example of a projectile. A cannonball shot from a cannon, a satellite orbiting the earth are also projectiles. 

To avoid confusion on projectile motion, let us treat the horizontal component and the vertical component of the motion separately.  If friction is negligible, the horizontal component of a projectile  motion is similar to a  ball moving a straight line in a constant velocity.

The vertical component of the projectile motion is similar to a ball moving as a free falling body. The velocity increases with time.

If we combine these components we will obtain a projectile motion. A projectile is simply a combination of a uniform horizontal motion and a uniformly accelerated vertical motion. The only force acting in the motion is the weight. The path of the projectile motion is known as the trajectory. When you kicked a ball with a certain angle and it landed to a certain point, the distance between the kick off point and the landing point is what you called the range.

For example, you kicked a soccer ball with an initial velocity of 42 m/s, 37⁰ from the horizontal. What is the maximum height the ball could reach? How long it will take for the ball to reach the maximum height? How long is the ball in air? What is the range?

First you need to get the x and y component of the velocity, v_o,

v_{ox = Vo}cosθ

v_{ox =} 42m/s cos 37⁰

v_{ox =}  33.54 m/s

v_{oy =} v_osinθ

v_{oy =} 42 m/s sin 37⁰

v_oy =  25.28 m/s

To get the height, we are going to use the equation

h = (v_1y ² - v_oy²)/ -2g

Remember that at the maximum height the velocity, v₁ is zero. Therefore

h = (v_1y ² - v_oy²)/ -2g

h =  - v_oy²/ -2g

h = (25.28m/s)² /-2 (9.8m/s²)

h = 32.6 m/s

To get the time to reach the maximum height we are going to use the equation

t = (v_1y  - v_oy)/ -g

At the maximum height, the velocity v₁ is zero. Therefore

t =  - v_oy/ -g

t =-25.28/-9.8 m/s²

t = 2.58s

The time the ball is in the air is

T = 2t

T = 2 (2.58s)

T = 5.16s

To get the range we are going to use the equation

R = v_ocosθT

R = (42 cos 30)(5.16s)

R = 173.03 m

Practical Applications:

If you are going to fire a gun horizontally and drop a bullet vertical with the same height with the gun, at the same time, which bullet will hit the ground first? Why do we need to avoid indiscriminate firing?

Predict, Observe, Explain

 Put a coin at a smooth table which is slightly hanged at the edge. Then put another coin near the overhanging coin. Flick the second coin across the table so that it strikes the overhanging coin and both coins now will fall on the floor. Which coin hits the floor first?

Physics Problem Sets: Valenzuela City Polytechnic College (AT-2, FSM-2, HVAC-R-2)

Physics Problem Sets. Love Physics!

1. An antelope moving with constant acceleration covers the distance between two points 80.0 m apart in 7.20s. Its speed as it passes the second point is 20.0 m/s. a) What is its speed at the first point? b) What is the acceleration?
2. The catapult of the aircraft carrier USS Abraham Lincoln accelerates an F/A – 18 Hornet jet fighter from rest to a take-off speed of 166 mi/h in a distance of 310 ft. Assume constant acceleration. a) Calculate the acceleration of the fighter in m/s2. b) Calculate the time required for the fighter to be accelerated to take-off speed.
3. An airplane travels 900m down the runway before taking off. If it starts from rest, moves with constant acceleration, and becomes airborne in 8.98 s, what is its speed in m/s, when takes off?
4. If a flea can jump straight up to a height of 0.520 m, what is its initial speed as it leaves the ground? b) For how much time is it in the air?
5. A player kicks a ball with a velocity of 40 m/s, 35º from the horizontal. Find:
a. the maximum height the ball could reach.
b. the time to reach the maximum height.
c. the time the ball is in the air.
d. the range.
6. A car has a mass of 2000 kg. It is traveling at a velocity of 14 m/s northward. A delivery truck with a mass of 3200 kg moving 18 m/s southward collided head-on with the delivery car. They stick together after collision. Find their common velocity after the collision.
7. A tricycle has a mass of 200 kg. If it has a velocity of 9 m/s northward, what is its momentum? If a car has a mass of 1800 kg, what should be its velocity to have the same momentum with the car.
8. A stone with a mass of 0.81 kg is attached to one end of a string 0.90 m long. The string will break if its tension exceeds 500N. The stone is whirled in a horizontal circle on a frictionless table top; the other end of the string is kept fixed. Find the maximum speed the stone can attain without breaking the string.
9. You dropped a 0.5kg ball from the top of 400m high building building. How much is the potential energy and kinetic energy of the ball just before hitting the ground. Use the Law of Conservation of Energy.
10. What is the pressure on the bottom of an aquarium 0.40 m deep filled with saltwater?


ENJOY PHYSICS CLASS! Enjoy Solving Physics Problems.
SOLVE THE FOLLOWING PHYSICS QUESTIONS AND SUBMIT IT TO YOUR PHYSICS CLASS ON SEPTEMBER 26, 2015  TO YOUR PHYSICS TEACHER.

Physics Problem Set: Valenzuela City Polytechnic College ET-2B

Physics Problem Sets. Love Physics!

1. An antelope moving with constant acceleration covers the distance between two points 80.0 m apart in 7.20s. Its speed as it passes the second point is 20.0 m/s. a) What is its speed at the first point? b) What is the acceleration?
2. The catapult of the aircraft carrier USS Abraham Lincoln accelerates an F/A – 18 Hornet jet fighter from rest to a take-off speed of 165 mi/h in a distance of 300 ft. Assume constant acceleration. a) Calculate the acceleration of the fighter in m/s2. b) Calculate the time required for the fighter to be accelerated to take-off speed.
3. An airplane travels 500m down the runway before taking off. If it starts from rest, moves with constant acceleration, and becomes airborne in 8.98 s, what is its speed in m/s, when takes off?
4. If a flea can jump straight up to a height of 0.520 m, what is its initial speed as it leaves the ground? b) For how much time is it in the air?
5. A player kicks a ball with a velocity of 42 m/s, 35º from the horizontal. Find:
a. the maximum height the ball could reach.
b. the time to reach the maximum height.
c. the time the ball is in the air.
d. the range.
6. A car has a mass of 2000 kg. It is traveling at a velocity of 14 m/s northward. A delivery truck with a mass of 3200 kg moving 18 m/s southward collided head-on with the delivery car. They stick together after collision. Find their common velocity after the collision.
7. A tricycle has a mass of 200 kg. If it has a velocity of 9 m/s northward, what is its momentum? If a car has a mass of 1800 kg, what should be its velocity to have the same momentum with the car.
8. A stone with a mass of 0.81 kg is attached to one end of a string 0.90 m long. The string will break if its tension exceeds 600N. The stone is whirled in a horizontal circle on a frictionless table top; the other end of the string is kept fixed. Find the maximum speed the stone can attain without breaking the string.
9. A nail weighs 0.2254 if it is in air and 0.1245N if it is submerged in oil with a density of 800 kg/m3. What is the density of the nail?
10. What is the pressure on the bottom of an aquarium 0.40 m deep filled with freshwater?


ENJOY PHYSICS CLASS! Enjoy Solving Physics Problems.
SOLVE THE FOLLOWING PHYSICS QUESTIONS AND SUBMIT IT TO YOUR PHYSICS CLASS ON SEPTEMBER 27, 2014  TO YOUR PHYSICS TEACHER.

Physics GFD - Valenzuela City Polytechnic College

Physics Problems!!! Enjoy Physics!!!

1. An antelope moving with constant acceleration covers the distance between two points 80.0 m apart in 7.00s. Its speed as it passes the second point is 20.0 m/s. a) What is its speed at the first point? b) What is the acceleration?
2. The catapult of the aircraft carrier USS Abraham Lincoln accelerates an F/A – 18 Hornet jet fighter from rest to a take-off speed of 170 mi/h in a distance of 320 ft. Assume constant acceleration. a) Calculate the acceleration of the fighter in m/s2. b) Calculate the time required for the fighter to be accelerated to take-off speed.
3. An airplane travels 500m down the runway before taking off. If it starts from rest, moves with constant acceleration, and becomes airborne in 8.98 s, what is its speed in m/s, when takes off?
4. If a flea can jump straight up to a height of 0.525 m, what is its initial speed as it leaves the ground? b) For how much time is it in the air?
5. A player kicks a ball with a velocity of 42 m/s, 37º from the horizontal. Find:
a. the maximum height the ball could reach.
b. the time to reach the maximum height.
c. the time the ball is in the air.
d. the range.
6. A car has a mass of 2000 kg. It is traveling at a velociyty of 15 m/s northward. A delivery truck with a mass of 3200 kg moving 18 m/s southward collided head-on with the delivery car. They stick together after collision. Find their common velocity after the collision.
7. A tricycle has a mass of 200 kg. If it has a velocity of 9 m/s northward, what is its momentum? If a car has a mass of 1800 kg, what should be its velocity to have the same momentum with the car.

Enjoy Physics!!!

Valenzuela Polytechnic College Environmental Science Investigative Project

Environmental Science Project by Computer Technology
Environmental Science Project by Electrical Technology

Physics Help: Ideas in the problem set in Physics

Ideas in Physics. Happy Solving!!!

1. Momentum is the product of mass and velocity.
2. The centripetal force in a uniform circular motion is equal to the product of mass and the square of the velocity over radius.
3, Pressure is equal to the density multiplied to the acceleration due to gravity and multiplied to the height.

Enjoy Physics!