Question

Solve the equation of motion, using Newton's 1 Law F 0, for a general case of M the mass of the wooden block and u, being the coefficient of static friction between the wooden block and the inclined table top, (note; this can be done at home as well, again your own text book is your first help). By solving we mean; find an expression for , in terms of other parameters. Generally, we can measure these other parameters, such as the M and the inclined your work toward finding this final expression.

Answer 1

Answer:

Explanation:

The first thing to have to make a diagram where we indicate the forces acting on the block, see attached. We have the following

  The weight (W) that is vertical

  The friction force (fr) that opposes the movement

  The driving force (F)

  The normal (N) which is the reaction to the support of the body and is perpendicular to the surface

We write a reference system where one axis is parallel to the surface (x axis) and the other is perpendicular to it (Y axis) we decompose the forces on these axes, we see that the only force we have to decompose r is the weight

             sin θ  = Wx / W       ⇒      Wx = W sin θ

             cos θ = Xy / W        ⇒      Wy = Wcos θ

We write Newton's equations for each axis

             N- Wy = 0

             F -fr -Wx = m a          (1)

The expression for the friction force is

             fr = μ N

             N = Wy

             N = W cos θ

             fr = μ mg cosT

   

We hope, we simplify the acceleration of equation 1

           a = F - μ mg cos θ -mg sinθ

           a = F - mg (μ cos θ -sin θ)

This is the general equation for movement.