Work done by a constant force

Work and energy

P = mg

Weight

P = mu

Momentum is a vector quantity that is in the direction of u and has dimensions of kg^. m/s.

Newton’s second law of motion states that:

The time rate of change of momentum of a particle is equal to the resultant external force acting on the particle:

Σ F = dp/dt = d/dt(mu) (2)

This is the most general form of Newton’s second law, which is valid in internal frame of reference. The notation Σ F represents the vector sum of all forces acting on the particle.

Since m is constant, then eq. (2) can be expressed

Σ F = d/dt(mu) = m du/dt (3)

Since acceleration is defined as a = du/dt, equation (3) can be written

Σ F = ma

The SI units of force is the newton

We are well aware of the fact that bodies are attracted to the earth. The force exerted by the earth on a body is called the weight of the body P. This force is directed toward the center of the earth.

We have seen that a freely falling body with a = g and F - P,gives

Since the weight depends on g, it varies with geographic location. Bodies weight less at higher altitudes than at sea level.

Newton’s third law

Newton’s third law states that if two bodies interact, the force exerted on body 1 by body 2 is equal to an opposite the force exerted on body 2 by body 1. This is

F₁₂ = - F₂₁

Consider an object that undergoes a displacements along a starting line under the action of a constant force F, which makes an angle α with s as fig.1

The work W done by the constant force is defined as the product of the component of the force in the direction of the displacement and the magnitude of the displacement.

Since the component of F in the direction of s is F cos α, the work W done by F is given by

W = (F cos α)s (1)

If an applied force F acts along the direction of the dispolacement, then α=0, and cos 0 = 1. In this case, Equation1 gives

Дата добавления: 2013-12-13