Image shows c is a straight line down and the dots are close together and get farther apart.

Free fall acceleration is constant and has a value of 9.8 m/s2.

The average accelerations, from most positive to most negative, are as follows: (B) 4 m/s2, (A) 3 m/s2, (D) 2.5 m/s2, and (C) ?3 m/s2.

If the yellow track were tilted steeply enough, its ball could win. How might you go about calculating the necessary change in tilt?

backward motion of the planets in the sky.

Sort the characteristics according to whether they are part of the geocentric model, the heliocentric model, or both solar system models.

Sort each statement according to whether it is an advantage of the heliocentric model, the geocentric model, or both.

The heliocentric model did not make noticeably better predictions than the geocentric model.

From Earth, all heavenly bodies appeared to circle around a stationary Earth.

Ancient astronomers did not observe stellar parallax, which would have provided evidence in favor of the heliocentric model.

force

momentum

acceleration

velocity

The sum of two vectors is the largest when the two vectors point in the same direction.

The x component of the resultant of two vectors is Ax+Bx.

To find the resultant of two vectors, add them tail-to-tip and then draw the resultant vector from the tail of the first vector to the tip of the last vector.

Because the sled’s velocity is constant, the net force must be zero and the two horizontal forces must balance out.

When the net force is zero, the acceleration is zero, so the velocity must be constant. Note that zero velocity is simply a special case of constant velocity.

An object moving in a straight line at constant speed has zero acceleration because the net force acting on it is also zero.

when you hold the ball still in your hands before it is thrown

When an object’s velocity is changing, the net force on it is not zero, even if it stops for an instant.

Since F = ma, the acceleration is given by a = F/m, so the object with the lower mass has a higher acceleration.

Since the net force is zero, the parachutist’s acceleration is zero, so the velocity is constant in time.

An object far from any source of gravity still has mass, even if no forces of gravity are acting on it.

Since the scale is pushing upward with a strength less than the force of gravity, the net force is directed downward, causing the person to decelerate.

Since the person is accelerating upward, the scale must be pushing upward more strongly than the force of gravity.

The acceleration is given by a = F/m, so all objects fall at the same rate since the force of gravity is proportional to the object’s mass.

Since the twin in the green jumpsuit (going head first) has a smaller surface area plowing through the air, she must fall faster in order for the force of air resistance to have the same strength as the force of gravity.

Since the red parachutist is more massive, he experiences a stronger force of gravity acting downward. In order for the wind resistance to balance this stronger force, he must have a faster terminal velocity.

Since the elevator is not accelerating, the reading on the scale is the same as in the video.

Since the attached rope doesn’t have to support any weight (as it did in the vertical case), the tension is the same in both ropes

The rocket’s speed is proportional to the ratio of the fluid’s mass to the rocket’s mass.

An object’s momentum is equal to the product of its mass and its velocity.

The momentum of an object is a vector quantity, and is defined as the product of the object’s mass and its velocity.

During the collision, the force exerted by the glue (on the eight-ball) cancels the force exerted by the cue ball (on the eight-ball). Thus, the momentum of the eight-ball system is conserved because the net external force acting on it is zero.

You might be confusing an “isolated” system with a system subject to “zero net force.” No external forces act on an isolated system. Is that the case for the eight-ball? For further review, see the discussion of systems in the video.

When the net external force on a system is zero, the system has zero acceleration and constant momentum.

In each collision, the change in momentum of the puck has the same magnitude as the change in momentum of the shoe. The puck has a greater magnitude of change in momentum when it rebounds, so the right shoe must undergo a greater change in momentum than the left shoe!

By doubling the mass but keeping the velocities unchanged, we doubled the angular momentum of the two-puck system. However, we also doubled the moment of inertia. Since L=I ?, the rotation rate of the two-puck system must remain unchanged.

The pendulum will swing back and forth more quickly (with a shorter period) because it is oscillating in a stronger gravitational field than that on Earth.

The kinetic energy of a moving object is always positive, regardless of the direction it is moving in, or the coordinate system used.

When an object’s displacement has a component in a direction opposite that of a given force, that force does negative work on the object.

When the net work done on an object is zero, there is no overall change in the object’s kinetic energy.

The person starts out with the same potential energy regardless of which slide she chooses, and all of this potential energy is converted to kinetic energy at the bottom of the slide. Therefore, the person must have the same kinetic energy at the bottom of each slide.

The kinetic energy is proportional to the ball’s mass times the speed squared. The 2-kg ball is moving twice as fast and is half as massive, so it will have twice as much kinetic energy as the 4-kg ball.

The ball is dropped from a distance twice as high, so it has twice as much energy (all of its energy is initially in the form of potential energy). This means that its final kinetic energy is twice as high. Since the kinetic energy is proportional to the square of the ball’s speed, its speed must be 2? faster.

The force of gravity weakens as the distance from the center of Earth increases (for changes in height that are small compared to the radius of the Earth, gravity can be approximated as being constant). Because of this weakening, the gravitational potential energy does not increase as quickly with height when the object is far away. As a result, the object doesn’t lose twice as much potential energy when it falls twice as far.

Thermal energy is the total kinetic energy of a substance due to all the random vibrational motions of the individual atoms. If the temperature were zero, none of the atoms would be moving.

As the cloud collapses, gravitational potential energy is converted into thermal energy, causing the gas to heat up.

The electron and proton have rest-mass energy (as well as some kinetic energy). All of this energy is converted into radiative energy.

Since the temperature is the same for both types of atoms, they have the same average kinetic energy, which is given by K=1/2mv2. Helium is twice as massive as hydrogen, so the average speed of the hydrogen atoms is 2? times higher than that of the helium atoms.

A body that is in free fall has only the force of gravity acting on it. The acceleration due to gravity is constant of 10m/s/s. The velocity is increasing as the object falls with 10m/s for every second.

Net force is always m•a. In this case, the velocity is constant so the acceleration is zero and the net force is zero. Constant velocity motion can always be associated with a zero net force.

Inertia is a body to keep doing what it is doing, therefor if the car comes to a stop your body was already moving and wants to keep moving. Inertia only depends on mass and is independent of acceleration, resistance and gravity.

At the top of the path the velocity has a magnitude of zero but it is changing direction due to acceleration. The acceleration acting on the ball during the entire path is the acceleration due to gravity (10m/s/s) and the only force (excluding air resistance) acting on it is the force due to gravity directed downward.

Vector is any concept with a magnitude and direction

Newton’s first law: if the net force (the vector sum of all forces acting on an object) is zero, then the velocity of the object is constant (same speed and same direction…straight line)

( Know this one. Kilograms is for mass and Newtons is for force.)

Mass depends on how much matter is present in an object. ( This is kind of a simple definition of mass but it does do the job (provided stuff means atoms or material).

The mass of an object is mathematically related to the weight of the object. (The weight of an object is the mass of the object multiplied by the acceleration of gravity of the object. Mass and weight are mathematically related by the equation: Weight (or Fgrav) = m•g)

Weight refers to a force experienced by an object. (This statement is true in the sense that the weight of an object refers to a force – it is the force of gravity.)

The weight of an object would be less on the Moon than on the Earth.

( The weight of an object depends upon the mass of the object and the acceleration of gravity value for the location where it is at. The acceleration of gravity on the moon is 1/6-th the value of g on Earth. As such, the weight of an object on the moon would be 6 times less than that on Earth.)

Velocity is speed and direction, Jack and Jill are traveling in the same direction but they have different speeds, so they will have different velocities.

The acceleration of gravity is approximately 10 m/s/s. Acceleration represents the rate at which the velocity changes – in this case, the velocity changes by 10 m/s every second. So the speed will increase by the amount of 10 m/s every second.

All that is necessary is that car A has a greater speed (is moving faster). If so, it will eventually catch up and pass car B. Acceleration is not necessary to overcome car B; a car going 60 mi/hr at a constant speed will eventually pass a car going 50 mi/hr at a constant speed. Surely you have witnessed that while driving down a local highway.

If an object is slowing down, then the direction of the acceleration vector is in the opposite direction as the direction which the object moves. (If the object were speeding up, the acceleration would be eastward.)

As an object falls, it accelerates; this means that the speed will be changing. While falling, the speed increases by 10 m/s every second. The acceleration is a constant value of 10 m/s/s; thus, choice b should not be chosen.

Since the speed of a free-falling object increases by 10 m/s every second, the speed after ten of these seconds will be 100 m/s.

The car is heading leftward and the velocity is always in the same direction as the direction which the object moves. Since the car is speeding up, the acceleration is leftward. Whenever an object speeds up, its acceleration is in the same direction which the object moves. Whenever an object slows down, its acceleration is in the opposite direction which the object moves.

The equation for gravitational force,

cites only masses and distances as variables. Rotation and atmospheres are irrelevant.

Speed being a scalar, and velocity being a vector quantity are irrelevant. Any moving object has both momentum and kinetic energy.

If you were moving up or down at a constant speed, your weight would not be more or less. It must be accelerating to cause a change in apparent weight.

After the collision, the mass of the moving freight cars has doubled. Can you see that their speed is half the initial velocity of freight car A?

Acceleration of a non-free fall is always less than g. Acceleration will actually be (20 N – 5 N)/2 kg = 7.5 m/s2.

Acceleration points inward

Velocity follows a straight path.

Distance = (1/2) x acceleration x time x time

So: Distance = (1/2) x 10 m/s2 x 4 s x 4 s

So: Distance = 80m

Two eight-horse teams could not pull the halves apart even though the hemispheres fell apart when air was readmitted.

Suppose von Güricke had tied both teams of horses to one side and bolted the other side to a trunk of a large tree (which did not move). In this case, the tension on the hemispheres would be:

The gain in kinetic energy, proportional to the square of the block’s speed at the bottom of the ramp, is equal to the loss in potential energy. This, in turn, is proportional to the height of the ramp.

Because force equals the time rate of change of momentum, the two balls lose momentum at the same rate. If both balls initially have the same momentum, it takes the same amount of time to stop them.

Conservation of momentum tells us that the changes in momentum must add up to zero. So the change in the car’s momentum must be equal to the change in the truck’s momentum, and the two changes must be in the opposite directions.

The cart comes to a stop when all of the cart’s kinetic energy is lost to friction. The frictional force times the stopping distance is equal to the cart’s initial kinetic energy.

always positive or zero

Ekin=12mv2

is by definition a quantity that can be only positive or equal to zero. It’s a scalar quantity, doesn’t have a direction, it’s a number that quantifies the “amount of motion” an object has.

These are all Newton’s Third Law pairs of forces, so they have to be equal.

During the collision, will the magnitude of the force exerted on truck A by truck B be _____ the magnitude of the force exerted on truck B by truck A?

Momentum is equal to force times time. Because the forces on the carts are equal, as are the times over which the forces act, the final momenta of the two carts are equal.

Pushing a chair

Lifting a water bottle

Ball being dropped

Lifting a book

The kinetic energy is proportional to the square of the speed. Therefore, doubling the speed quadruples the kinetic energy.

Let’s say the ball has inertial mass m and velocity v. The decrease in momentum in case (i) is 0 – mv = -mv (final momentum minus initial momentum). In case (ii), we find mv – 0 = +mv. In case (iii), we have m(-v) – mv = -2mv because the ball’s velocity is now in the opposite direction. So the magnitude of the change is greatest in the third case.

Both frogs reach the same maximum height.