Question

A museum curator moves artifacts into place on various different display surfaces. If the curator moves a 145 kg aluminum sculpture across a horizontal steel platform what is fs, fmax, and fk

Answer 1

Static friction is,
`0\ N\leq f_s\leq 866.81\ N`

Maximum static friction is,
`f_(max)= 866.81\ N`

Kinetic friction is,
`f_k=667.87\ N`

Step-by-step explanation:

The value of coefficient of static friction between Aluminium and Steel is
`\mu_s=0.61` and the value of coefficient of kinetic friction is
`\mu_k=0.47`

Given:

Mass of the sculpture is,
`m=145\ kg`.

As the sculpture is moved along the horizontal direction only, there will no net force acting along the vertical direction. Therefore,

Normal force by the steel platform will be equal to the weight of the aluminium sculpture. That is,

`N=mg`

Now, the static friction is given as the product of normal force and coefficient of static friction. The static friction varies from a value of 0 to limiting friction.

The limiting friction is the maximum static friction that acts on a body to resist the motion.

The value of the limiting friction or the maximum static friction is given as:

`f_(max)=\mu_sN=\mu_smg=0.61* 145* 9.8=866.81\ N`

Thus, static friction is given as:

`0\leq f_s\leq f_(max)\\0\leq f_s\leq \mu_smg\\0\ N\leq f_s\leq 866.81\ N`

Now, kinetic friction is the frictional force acting on a body when the body is moving under the action of forces. Thus kinetic friction is the product of normal force and coefficient of kinetic friction. Kinetic friction is a constant opposing force.

Thus, kinetic friction is given as:

`f_k=\mu_kN\\f_k=\mu_kmg\\f_k=0.47* 145* 9.8=667.87\ N`