As the angle between the direction of the applied force in the direction of movement increases from zero to ninety what happens to the fraction of the force that contributes to the work?

As the angle between the direction of the applied force and the direction of movement increases from zero to ninety degrees, the fraction of the force that contributes to the work decreases.

To understand this concept, let's consider the work done by a force. The work done by a force can be calculated using the formula:

Work = Force * Distance * cos(θ),

where θ is the angle between the force vector and the displacement vector.

When the angle θ is zero degrees (or very close to zero), the force is directly applied in the direction of movement. In this case, the entire force contributes to the work done, and the cosine of 0° is equal to 1.

As the angle θ increases towards 90 degrees, the force vector becomes more perpendicular to the direction of movement. In this scenario, the cosine of θ decreases, resulting in a smaller fraction of the force contributing to the work. When the angle θ is 90 degrees, the force is applied perpendicular to the direction of movement, and the cosine of 90° is 0. Therefore, no work is done by the force on the object in this situation.

In summary, as the angle between the direction of the applied force and the direction of movement increases from zero to ninety degrees, the fraction of the force that contributes to the work decreases gradually.

When the angle between the direction of the applied force and the direction of movement increases from zero to ninety degrees, the fraction of the force that contributes to the work decreases.

To understand why, let's consider a situation where an object is being pushed or pulled along a surface. The work done on an object is given by the formula: Work = force * distance * cos(theta), where theta is the angle between the direction of the applied force and the direction of movement.

When the angle theta is zero degrees, the force and the direction of movement are aligned. In this case, the entire force is contributing to the work done on the object. This means that the fraction of the force that contributes to the work is 100%.

As the angle theta increases from zero to ninety degrees, the force starts to deviate more and more from the direction of movement. This causes the component of the force that is parallel to the direction of movement to decrease. The work done on the object is only determined by the force component that is parallel to the direction of movement, as given by the formula above.

At an angle of ninety degrees, the force is entirely perpendicular to the direction of movement, which means no work is done on the object since there is no force component acting in the direction of movement. In this case, the fraction of the force that contributes to the work is 0%.

Therefore, as the angle between the direction of the applied force and the direction of movement increases from zero to ninety degrees, the fraction of the force that contributes to the work decreases from 100% to 0%.