Physical Science Lesson 1

Seite 1

A researcher observes a vehicle with an initial velocity of 14 m/s. The vehicle accelerates uniformly with an acceleration of 3 m/s2. After 6 seconds, what is the velocity of the vehicle?v2 = v1 + at

v2 = 14 m/s + (3 m/s^2 × 6 s)

Deceleration formula:

a=v2-v1/t

On Earth, acceleration from gravity is always 9.8m/s^2 this is abbreviated "g" in equations.

This is accurate when ignoring air resistance

A free-falling body is an example of body movement with uniform acceleration and is assumed to have an acceleration due to the force of earths gravity. Gravity acceleration has the symbol g in the formulas and is measured in m/s^2.

All formulas for calculating the final velocity, time, and distance of a body moving with uniform acceleration can be applied to falling bodies if the following conditions are observed:

1. Assume that the gravity acceleration g is a constant (unvarying rate of acceleration throughout the fall).

2. Ignore air resistance.

For calculations in this course, ignore the resistance of air even though it affects acceleration.

a=v2−v1t

In this formula, a stands for acceleration, t stands for the time interval, v2 stands for velocity at the end of the time interval t, and v1 stands for velocity at the beginning of the time interval t.

In general, acceleration is expressed as length units per time unit squared.

the formula for uniform velocity to calculate the answer, and solve for distance (s) instead of velocity.

s = v × t

The velocity of a body can be determined by the following formula:

v=s/t

v stands for velocity in meters per second, s stands for distance in meters, and t stands for time in seconds.

the average velocity may be calculated with the following formula:

vav=v1+v2/2

In this formula, vav stands for the average velocity during a time interval, v1 stands for the original velocity, and v2 stands for the final velocity.

The formula t=s/v, is a variation of the velocity formula, can be used to solve this problem.

A body can be solid, liquid, or gaseous. Force causes motion in a linear (straight) or curved path.

The metric system consists of liters, meters, and grams; the English system uses pounds, feet, and quarts.

Speed is the distance a body travels in a certain time; velocity includes direction of travel as well as distance covered in a unit of time. v = s ÷ t.

When a car is traveling a certain number of miles per hour, this is its average speed across a distance, as it may move faster or slower from moment to moment. Instantaneous speed is the speed at a particular moment in time.

Uniform velocity refers to the speed of a body if it covers the same distance within equal intervals of time going a fixed direction. This can be plotted on a graph.

Acceleration is a velocity change during a unit of time.

Acceleration of a falling body, or gravity, is 9.8 m/s^2.

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Newton’s First Law of Motion: A body at rest or in motion at a constant speed tends to remain at rest or in motion at constant speed unless acted upon by some external force.

Newton’s Second Law of Motion describes what happens to a body when external forces act on it: When an external force acts on a body, that body is accelerated with a magnitude proportional to the force and inversely proportional to the mass. In the form of an equation, this law can be expressed as:

a=F/m or

F = ma

In this formula, a stands for acceleration in meters per second squared, F stands for force in newtons, and m stands for mass in kilograms.

Uniform acceleration is acceleration due to gravity. If gravity acceleration g is substituted for general acceleration a in the equation of Newton’s second law, the equation becomes

F = mg

In this formula, F stands for the force of gravity in newtons, m stands for mass in kilograms, and g stands for gravity acceleration (9.8 m/s^2).

The force measured by this equation is the force acting on a body and causing the earth’s gravity acceleration; it’s called the force of gravity, or gravity.

the direction of the force causing acceleration is in the same direction as the acceleration.

In a scientific discussion of mechanics, the term “weight” should either be avoided or used only to indicate the force of gravity that acts upon a mass.

When metric units are used, the confusion between mass and force of gravity is easily avoided. Mass is measured in kilograms and the force of gravity is measured in newtons. A quantity expressed in kilograms, grams, or megagrams is the mass; a quantity expressed in newtons is a force—including the force of gravity, or “weight.”

Newton’s second law states that if an external force is exerted on a body, the body will be accelerated. However, if the body isn’t free to move, it will push back with an equal force. Under those conditions, there will be no net external force acting on the body and the body won’t move.

Newton’s Third Law of Motion: Whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body. It’s usually stated as Every action has an equal and opposite reaction.

If a measurement is a vector it has a magnitude and a direction:

Velocity: 12m/s east

Force: 5 newtons at a 30* angle

Acceleration: -9.8m/s^2

If a measurement is a scalar it only has a magnitude:

Speed: 1 mile per hour

Time: 7 seconds

Temperature: 32 degrees Fahrenheit

a force of 10 newtons (N) is applied to a ball with a mass of 0.5 kilograms (kg). What is the acceleration of the ball?

Solution: Use the formula for Newton’s second law to solve the problem. Substitute the given values into the formula, then solve.

a=Fma=Fm

a=10 N0.5 kga=10 N0.5 kg

a = 20m/s^2

Suppose that a force of 100 N causes a body to move with an acceleration of 5 m/s2. What is the mass of the body?

Solution: Use a variation of the formula for Newton’s second law to solve for mass. Substitute the given values into the formula, then solve.

m=F/a

m = 100 N ÷ 5 m/s^2

m = 20kg

What force (in newtons) is required to accelerate a body with a mass of 10 kilograms at a rate of 6 m/s2?

Solution: Use a variation of the formula for Newton’s second law to solve for force. Substitute the given values into the formula, then solve.

F = ma

F = 10 kg × 6 m/s^2

F = 60 N

An astronaut’s body has a mass of 70 kilograms. What is the force of gravity acting on his mass (that is, his “weight”) on earth?

Solution: Use the force formula. Substitute the known values into the formula and solve. (If not indicated otherwise, assume that g = 9.8 m/s2.)

F = mg

F = 70 kg × 9.8 m/s^2

F = 686 N

What is the force of gravity (the “weight”) of the same astronaut on the moon?

Solution: Use the force formula to solve this problem. Substitute the known values into the formula and solve.

F = mg

F = 70 kg × 9.8 m/s2

F = 686 N

Next, divide the answer by six, because the force of gravity on the moon is about one-sixth of the force of gravity on the earth.

F = 686 N ÷ 6

F = 114.3 N

Answer: The force of gravity acting on the astronaut on the moon is 114.3 newtons.

To find the force of gravity on the moon, combine the formula and the division into one step:

F=mg/6

Using the previous example, review the steps.

F=mg/6

F=70kg×9.8m/s^2 /6

F=686/6

F = 114.3 N

The force of gravity acting on a girl’s mass on Earth is 550 newtons. What is her mass?

Solution: Use a variation of the force formula to solve for mass. Substitute the known values into the formula and solve.

m=F/g

m=550N/9.8m/s^2

m = 56.123 kg, or, rounded, 56 kg

Change in motion (acceleration) is related to two things:

the mass of the body

the force acting on it.

the formulas used:

a=f/m

f=mXa

m=f/a

d acceleration in m/s^2

f is force in Newtons

m is mass in kilograms

Newton’s First Law of Motion states that a body at rest tends to remain at rest.

Newton’s Second Law of Motion relates mass and force to acceleration. This law can be expressed in an equation, a = F ÷ m.

Force occurs in pairs; every action has an equal and opposite reaction.

A vector is a quantity that has both magnitude and direction. A scalar is a quantity used to measure magnitude.

Seite 3

A centripetal force can be the following:

an object being whirled on a string, the tension in the string is the centripetal force.

Friction is the centripetal force when a car drives in a circle.

Supporting force is centripetal for a car on a bank turn, clothes in a washing machine, or a roller coaster on a loop.

Gravity if the centripetal force for a satellite or planet in orbit.

If the centripetal force stops, the object will move outward in a straight line instead of in a circle.

The gravitational force is directly proportional to the products of the masses:

masses increase, the force will increase.

The gravitational force is inversely proportional tot eh distance between the bodies:

Distance increase, the force will decrease.

Kepler's Laws:

1. the planets do not orbit in a perfect circle, their orbits are oval (ellipses).

2. the speed of the planets change during orbit. a line drawn from the planet to the sun makes equal areas in equal amounts of time

3. certain ratios describing the orbits are the same for every planet in the solar system.

A satellite is a body that orbits another body in space. whether its a man-made satellite or the moon

Centripetal force is a center-seeking force. An inclined roadbed helps to provide centripetal force.

The centripetal force that keeps the moon and satellites in orbit is gravity.

Ptolemy developed the model of a stationary earth. Copernicus theorized the rotation of the earth and other planets. Kepler introduced the idea of elliptical orbits.

The universal gravitational law states that every object that has mass attracts every other object that has mass.

Seite 4

The equation for momentum is

momentum = mass × velocity

or

p = mv

The letter p is used for momentum so it’s not confused with m for mass.

momentum formula:

p=mv

mass formula:

m=p/v

velocity formula:

v=p/m

Momentum: mass in motion. a measure of how difficult something is to stop.

doubling the mass or doubling the speed doubles the momentum.

In physics, different types of collisions are classified by what happens to the momentum of the two objects.

In an elastic collision, two objects hit each other and bounce apart. The total momentum of the system is generally conserved. If one object is moving and the other is still, after the collision, both objects will be moving but with a slower speed than the original object.

In an inelastic collision, the objects don’t bounce away from each other. a figure skater on the ice who is going fast and about to fall reaches out and grabs his friend, they’ll stick together and both start moving now weighing more combined (more mass), they’ll slow down in order to keep the same momentum.

the momentum of individual objects can change but the sum will be the same just distributed.

an inelastic collision is when objects collide and stick together to become a bigger mass

A truck that weighs 1,000 kg is traveling 5 m/s. What would happen to the vehicle’s momentum if the truck added a trailer that has a mass of an additional 1,000 kg but still traveled at 5 m/s?

1. Begin by figuring out the truck’s starting momentum, before the trailer.

Since the equation is p =mv, and you’re trying to find p, you know that the mass of the truck is 1,000 kg and the velocity is 5 m/s.

p = 1,000 kg × 5 m/s

p = 5,000 kg-m/s

2. Now, find the truck’s new momentum once it tows the trailer, which increases its mass.

p = (1,000 kg + 1,000 kg) × 5 m/s

p = 2,000 kg × 5 m/s

p = 10,000 kg-m/s

3. Compare your answers. You can see that once the truck tows the trailer, its momentum actually doubles. This makes sense because the truck’s mass doubled with the trailer.

Figure skater 1 weighs 50 kg with a speed of 2 m/s

p = mv (50kg × 2 m/s)

p = 100 kg-m/s (momentum)

Once the skater grabs his friend, they now have a total mass of 100 kg. Momentum must be conserved.

how fast are the skaters moving together? Solve for v in the equation for momentum. Use the original momentum of skater 1 but the total mass of both skaters, once they stick together.

100 = 100 kg × v

Solving for v, we get a velocity of 1 m/ s, which is slower than the 2 m/s that skater 1 was going

Two figure skaters:

if he has a mass of 50kg and is moving 3 meters per second, and she has a mass of 40kg and is moving 2 meters per second then they collide and he picks her up, we can solve to find the velocity of the pair once they are together.

find his momentum and her momentum add them together to get a total momentum. then after the collision, add together the masses of both people. now the equation is 230kgm/s = 90kg x velocity. to solve for velocity divide 230 by 90 for an answer of 2.5 meters per second.

Momentum is defined as an object’s mass multiplied by its velocity.

Objects have momentum when they're moving.

Momentum can be transferred between objects when they collide.

Multiple types of collisions can occur between objects:

A moving object can strike a stationary object, causing the still object to move and the first object to bounce back or to stop moving.

A moving object can strike a stationary object and stick to it; both objects then move together.

Two objects moving can collide with each other.

Conserved momentum means that all of the momentum in a system is constant both before and after a collision.