# What is the relationship between force and speed squared

### What is the Relationship Between Force Mass And Acceleration? | Sciencing

Investigate the relationship between centripetal force and velocity in circular motion, when a When we do that the uncertainties on “V” must be squared. Force equals mass times acceleration, or f = ma. to accelerate a 1-kilogram mass one meter per second squared. When an object gains speed, its acceleration is positive; when speed is lost, acceleration is negative. How can energy go up as the square of the velocity? rigorous and you'll find that the relationship between energy and velocity is exactly v^2. Instead of a single distance with a constant force, we chop up the distance into.

### Q: Why does kinetic energy increase as velocity squared? | Ask a Mathematician / Ask a Physicist

The original question was: I ran into these in physics class long ago and was really bothered by the first formula. How can energy go up as the square of the velocity? Worse, you would think that momentum would go up hand in hand with kinetic energy, when the formulas above instead show the latter going up much faster due to the exponent. This is pretty unintuitive.

## Q: Why does kinetic energy increase as velocity squared?

In fact, historically this was a whole thing. Buckets of profoundly smart folk argued and debated about whether velocity momentum or velocity squared energy was the conserved quantity.

The difficulty is first that energy can change forms and second that up until the 20th century lab equipment was terrible and often home-made. Force is mass times acceleration: If you apply a force over a time you get momentum and if you apply force over a distance you get energy.

Acceleration times time is velocity, so it should more-or-less make sense that force times time is momentum: If it falls twice as far it gains twice the energy.

A decent way to think about force and kinetic energy is to consider a falling weight. Gravity applies a constant force and thus a constant acceleration. If you tie a string to that weight you could power, say, a clock. This is particularly helpful and easy to use if you know that it starts with zero velocity just divide the final velocity in half. This is a simple re-write of the old distance-equals-rate-times-time formula with average velocity defined as above.

This is a very important formula for later use. It can be used to calculate an object's displacement using initial velocity, constant acceleration, and time. Though a bit more complex looking, this equation is really an excellent way to find final velocity knowing only initial velocity, average acceleration, and displacement.

Don't forget to take the square-root to finish solving for vf. This equation is the definition of a vector in this case, the vector A through its vertical and horizontal components. Recall that x is horizontal and y is vertical. This equation relates the lengths of the vector and its components. It is taken directly from the Pythagorean theorem relating the side lengths of a right triangle.

The length of a vector's horizontal component can be found by knowing the length of the vector and the angle it makes with the positive-x axis in this case, the Greek letter theta.

The length of a vector's vertical component can be found by knowing the length of the vector and the angle it makes with the positive-x axis in this case, the Greek letter theta. Because the components of a vector are perpendicular to each other, and they form a right triangle with the vector as the hypotenuse, the tangent of the vector's angle with the positive-x axis is equal to the ratio of the vertical component length to the horizontal component length.

This is useful for calculating the angle that a vector is pointed when only the components are known. This is Newton's Second Law, written as a definition of the term "force". Simply put, a force is what is required to cause a mass to accelerate. Since 'g' is already a negative value, we don't have to mess around with putting a negative to show direction down is negative in our x-y reference frame. Through experimentation, physicists came to learn that the frictional force between two surfaces depends on two things: These two factors are seen here in this equation: Since both are positive, we must include a negative to account for friction's oppositional nature always goes against motion.

Another way to interpret Newton's 2nd Law is to say that the net sum total force on an object is what causes its acceleration. Hence, there may be any number of forces acting on an object, but it is the resultant of all of them that actually causes any acceleration. Remember, however, that these are force vectors, not just numbers.

### Force, Mass, Acceleration | Zona Land Education

We must add them just as we would add vectors. A simple if-then statement that holds true due to Newton's 2nd Law. If the mass is not accelerated meaning: This is not to say that there is no force acting on it, just that the sum total of all the forces acting on it is equal to zero -- all the forces "cancel out".

Since force is a vector, I can simply focus on its components when I wish. So, if I have a series of forces acting on a mass, the sum of their x-components must be equal to the x-component of the net force on the mass. And, by Newton's 2nd Law, this must be equal to the mass times the x-component of the acceleration since mass has no direction, and acceleration is also a vector.

Similarly as above, if I have a series of forces acting on a mass, the sum of their y-components must be equal to the y-component of the net force on the mass. And, by Newton's 2nd Law, this must be equal to the mass times the y-component of the acceleration since mass has no direction, and acceleration is also a vector. If we calculate or just know the x- and y-components of the net force acting on an object, it is a snap to find the total net force.

As with any vector, it is merely the sum of its components added together like a right triangle, of course. This equation becomes ridiculously easy to use if either one of the components is zero. The definition of momentum is simply mass times velocity. Take note that an object can have different velocities measured from different reference frames. Newton's 2nd Law re-written as an expression of momentum change. This is actually how Newton first thought of his law.

It allows us to think of momentum change as "impulse" force over some timeand apply the law in a much simpler fashion. In a closed, isolated system, the total momentum of all the objects does not change. Since "closed" means nothing coming in or going out, we can imagine all our applications talking about a fixed set of objects.

Since "isolated" means no interactions with anything outside the system, we must imagine all our applications involve nothing but those objects and forces that we consider. In two dimensions, the law still holds -- we just pay attention to the components of the total momentum.

Here, a' refers to object a after the collision. This equation shows the relationship between arclength sradius rand angle theta - measured in radians. It is useful for finding the distance around any circular path or portion thereof at a given radial distance. This equation shows the relationship between the period of a pendulum and its length. It was first discovered by Galileo that the arc of a pendulums swing and the mass at the end of a pendulum do not factor noticeably into the amount of time each swing takes.

Only the length of the pendulum matters. The tangential velocity of an object in uniform unchanging circular motion is how fast it is moving tangent to the circle. Literally the distance around the circle divided by the period of rotation time for one full rotation. The centripetal acceleration of an object in uniform circular motion is how much its velocity because of direction, not speed changes toward the center of the circle in order for it to continue moving in a circle.

The force that is required to keep an object moving in a circular path is the centripetal force acting on the object. This force, directed towards the center of the circle, is really just a derivative of Newton's 2nd Law using centripetal acceleration.

The work done on an object is found by multiplying force and distance, but there is a catch. The force and distance must be parallel to each other. Only the component of the force in the same direction as the distance traveled does any work. Hence, if a force applied is perpendicular to the distance traveled, no work is done. The equation becomes force times distance times the cosine of the angle between them. Work is measured in units of newtons times meters, or joules J. Power is a physical quantity equal to the rate at which work is done.

The more time it takes to do the same work, the smaller the power generated, and vice-versa. Power is measured in units of joules per second, or watts W. Kinetic energy is simply the energy of motion - the more something is moving or the more there is to that somethingthe more kinetic energy it possesses.