IGCSE & A Level Physics with MO

Circular Motion
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It is a common misconception that objects have to move in the direction of the force. This is false; the acceleration points in the direction of the force. This means the change in velocity points in the direction of the force. It is not the velocity that points in the direction of the force.

For example, as the man approaches the top of the loop, he has very some upwards velocity from running up through the curve. At the apex, all that vertical velocity is converted into horizontal, and his vertical velocity is very small. At this point, gravity begins to act and increases his downward velocity.

However, gravity can only increase that downward velocity so fast. Before gravity can make him start falling, the much larger horizontal velocity allows the man to reach the downwards sloping part of the curve, which will accelerate him downwards faster.

Because of this, gravity will not make the man lose contact with the loop (assuming the man is going fast enough).

A similar system you can think of that you are probably familiar with is projectile motion. At the top of the trajectory the force points down, the velocity is horizontal, and the projectile continues on its parabolic path with both horizontal and vertical velocity. The difference between the projectile and the man in this example is that the net force is constant for the projectile. The horizontal component of the velocity never changes.

For the man, the net force is always changing so that the motion is circular. The vertical and horizontal components of the velocity are always changing around the circle. The projectile is falling, but the man isn't purely falling.
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Physics with Mo

Rotation and Revolution
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"Rotation" refers to an object's spinning motion about its own axis. "Revolution" refers to the object's orbital motion around another object. For example, Earth rotates on its own axis, producing a 24-hour day. Earth revolves around the Sun, producing the 365-day year. A satellite revolves around a planet.

Energy Transformation on a Roller Coaster
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A roller coaster ride is a thrilling experience which involves a wealth of physics. Part of the physics of a roller coaster is the physics of work and energy. The ride often begins as a chain and motor (or other mechanical device) exerts a force on the train of cars to lift the train to the top of a very tall hill. Once the cars are lifted to the top of the hill, gravity takes over and the remainder of the ride is an experience in energy transformation.

At the top of the hill, the cars possess a large quantity of potential energy. Potential energy - the energy of vertical position - is dependent upon the mass of the object and the height of the object. The car's large quantity of potential energy is due to the fact that they are elevated to a large height above the ground.

As the cars descend the first drop they lose much of this potential energy in accord with their loss of height. The cars subsequently gain kinetic energy.

Kinetic energy - the energy of motion - is dependent upon the mass of the object and the speed of the object. The train of coaster cars speeds up as they lose height. Thus, their original potential energy (due to their large height) is transformed into kinetic energy (revealed by their high speeds).

Once a roller coaster has reached its initial summit and begins its descent through loops, turns and smaller hills, the only forces acting upon the coaster cars are the force of gravity, the normal force and dissipative forces such as air resistance.

The force of gravity is an internal force and thus any work done by it does not change the total mechanical energy of the train of cars.

The normal force of the track pushing up on the cars is an external force. However, it is at all times directed perpendicular to the motion of the cars and thus is incapable of doing any work upon the train of cars.

Finally, the air resistance force is capable of doing work upon the cars and thus draining a small amount of energy from the total mechanical energy which the cars possess. However, due to the complexity of this force and its small contribution to the large quantity of energy possessed by the cars, it is often neglected. By neglecting the influence of air resistance, it can be said that the total mechanical energy of the train of cars is conserved during the ride.

That is to say, the total amount of mechanical energy (kinetic plus potential) possessed by the cars is the same throughout the ride. Energy is neither gained nor lost, only transformed from kinetic energy to potential energy and vice versa.

Pressure changes – and temperature
(at a constant volume)
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Pressure is directly proportional to Temperature:
Increasing the temperature of a gas increases the pressure.
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If a gas is heated, the particles move (faster) and have more (kinetic energy). As the KE increases, the particles (hit) the container walls (harder and more often), resulting in more (pressure).

This is also known as Gay-Lussac's Law, which states that

"The pressure of a given mass of gas varies directly with the absolute temperature of the gas, when the volume is kept constant."

Motion Question
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A blue car moving at a constant speed of 10 m/s passes a red car that is at rest. This occurs at a stoplight the moment that the light turns green. The clock is reset to 0 seconds and the velocity-time data for both cars are collected and plotted. The red car accelerates from rest at 4 m/s/s for three seconds and then maintains a constant speed. The blue car maintains a constant speed of 10 m/s for the entire 12 seconds. Observe the motion and make meaning of the accompanying graphs to answer the following questions:
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1-What is the final velocity of a car that accelerates from rest at 4 m/s/s for three seconds?

2-What is the displacement of each individual car after three seconds? (Consider a kinematic equation or the area of the velocity-time graph.)

3-What is the slope of the line for the red car for the first three seconds?

4-What is the displacement of each individual car after nine seconds (use the area of the velocity-time graph)?

5-Does the red car pass the blue car at three seconds? If not, then

6-when does the red car pass the blue car?

7-When lines on a velocity-time graph intersect, does it mean that the two cars are passing by each other? If not, what does it mean?

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Answers to above questions:

1- 12 m/s

2- Red Car: Area of Triangle = 0.5*b*h = 0.5*(3 s)*(12 m/s) = 18 m

3- Blue Car: Area of Rectangle = b*h = (3 s)*(10 m/s) = 30 m

4- slope = rise/run = (12 m/s- 0 m/s) / (3 s) = 4 m/s/s

5- Red Car: Area of Triangle + Area of Rectangle = 0.5*b1*h1 + b2*h2 = 0.5*(3 s)*(12 m/s) +(6 s)*(12 m/s) = 18 m + 72 m = 90 m

6- Blue Car: Area of Rectangle = b*h = (9 s)*(10 m/s) = 90 m

7- No! The red car passes the blue car at 9 seconds.

No! When lines intersect on a velocity-time graph, it means that the two cars have the same velocity. When lines intersect on a position-time graph, it means that the two cars are passing each other.

Position Time Graph for two cars at different Velocities
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Observe the two cars below.
The blue car starts ahead of" the red car.
(The red car actually starts off the screen.) Since the red car is moving faster, it eventually catches up with and passes the blue car.

Observe the position-time graphs for these two cars. The position-time plot of each car's motion is depicted by a diagonal line with a constant slope. This diagonal line is an indicator of a constant velocity.

At the time that the cars are side by side, the lines intersect. That is, the two cars share the same position at that instant in time.

The lines would not intersect for a velocity vs. time graph; there is never an instant in time in which they share the same velocity.

The two cars have the same position at seven seconds; yet they never have the same velocity at any instant in time.