# The relationship between work and kinetic energy

The initial velocity of the shot at the moment of the throw was 12,88 m/s, as it follows from the relation between work and the change of kinetic energy. Answer to What is the relationship between work and kinetic energy for a the sign of work done by gravity compare to the work done by the applied force?. Kinetic energy is a scalar. The units are the same as for work (i.e. Joules, J). Relation bewteen KE and W: The work done on an object by a net force equals the.

We could just find the individual amounts of work done by each particular force and add them up.

### Work and the work-energy principle (video) | Khan Academy

But there's actually a trick to figuring out the net work done on an object. To keep things simple, let's assume that all the forces already lie along the direction of the displacement. That way we can get rid of the cosine theta term. Since we're talking about the net work done on an object, I'm going to replace F with the net force on that object. Now, we know that the net force is always equal to the mass times the acceleration. So we replace F net with m times a.

So we find that the net work is equal to the mass times the acceleration times the displacement. I want to write this equation in terms of the velocities and not the acceleration times the displacement. So I'm going to ask you recall a 1-D kinematics equation that looked like this.

## Relationship between Work and Mechanical Energy

The final velocity squared equals the initial velocity squared plus 2 times the acceleration times the displacement. In order to use this kinematic formula, we've got to assume that the acceleration is constant, which means we're assuming that the net force on this object is constant.

Even though it seems like we're making a lot of assumptions here, getting rid of the cosine theta and assuming the forces are constant, none of those assumptions are actually required to derive the result we're going to attain.

They just make this derivation a lot simpler. So looking at this kinematic formula, we see that it also has acceleration times displacement. So I'm just going to isolate the acceleration times the displacement on one side of the equation and I get that a times d equals v final squared minus v initial squared divided by 2. Since this is what a times d equals, I can replace the a times d in my net work formula. And I find that the net work is equal to the mass times the quantity v final squared minus v initial squared divided by 2.

So you'll often hear that the net work done on an object is equal to the change in the kinetic energy of that object. And this expression is often called the work energy principle, since it relates the net work done on an object to the kinetic energy gained or lost by that object.

### Kinetics • Relation between work and energy

If the net work done is positive, the kinetic energy is going to increase and the object's going to speed up. If the net work done on an object is negative, the kinetic energy of that object is going to decrease, which means it's going to slow down. What was the velocity vodhod of the shot weighing 7,26 kg at the moment of the throw? The increase in the mechanical energy of the shot equals only the increase in its kinetic energy, because we decided to neglect its potential energy In order to maximize kinetic energy of human body or sport equipment we must exert the greatest possible force along the longest possible distance.

This way we can make us of the knowledge of the relation between energy and work to improve our technique in certain sports, especially in athletics. According to the relation between work and energy the velocity is maximized by the greatest possible force acting along the longest possible distance. Shot-putters therefore often start their throw by standing on one foot, bent forward over the edge of the shot-put circle, with their back towards the direction of the throw, to maximize the distance along which their force will act on the shot and thus to also maximize the initial velocity of the shot at the moment of the throw Fig.

The longer distance along which the force acts on the shot and the ability to use larger muscle groups thus leads to longer throws and better results.

Figure 13 Initial phases of shot put allowing to maximize the work performed during the throw. This happens mostly in catching projectiles, landing, etc.

Human muscles also perform negative work when our body lands on the ground. During landing it is important to maximize the distance along which the projectile is decelerating. By making stopping distance longer we make impact forces smaller. We must realize, however, that prolonging the stopping distance by bending our knees deeply, for example, does not necessary lead to smaller reaction forces in specific joints. To decrease impact forces and increase stopping distance we also use various materials: This law can be used in studying the motion of projectiles.

This kinetic energy is transformed into deformation energy of the pole and subsequently into the increase in potential energy of the athlete. In other words, the faster the pole vaulter runs and the better his pole is able to transform kinetic energy into potential energy through deformation energy, the higher he jumps. Part of energy is of course transformed in other types of energy, for example internal energy of the pole, resulting in heat.

In mechanics such ability is described by the quantity called power