Chapter 5, Problem 107A

To determine

To write:A physical problem for the graph that is a part of the solution.

Explanation of Solution

Given:

The given graph is shown below.

  

Consider an object is placed on sloping surface and is at rest. The force which is acting perpendicular to the surface of the object passing through the center of gravity of the object, in the upward direction is known as normal force. Then, the friction existing between the object and the surface is known as static friction.When a force is applied to push the object down the sliding surface, such that the magnitude of the force is more than the static frictional force existing between the surface and the object, then the object will slide downward and dynamic or kinetic frictional force comes into existence between the sliding surface and the object.

Consider the following physics problem for the given graph.

Consider an object of mass $10\text{kg}$ is pulled by a person over the surface shown below.

  

Find the force $\left(F\right)$ exerted by the person to pull the object. (Take the acceleration due to gravity $g=9.80{\text{m/s}}^2$ and coefficient of kinetic friction as ${\mu }_{\text{k}}=0.40$ ).

To solve this physical problem, initially the free body diagram of the situation has to be drawn to understand the forces acting on the object.

Consider the object is placed at the origin of the $x-y$ coordinate system.

Show the free body diagram of the situation as follows:

  

From the figure, the force $\left(F\right)$ required by the person to pull the object can be found using the relation,

  $\begin{array}{l}{F}_{\text{kinetic friction}}=F\cos \theta \\ \left({\mu }_{\text{k}}{F}_{\text{N}}\right)=F\cos \theta \\ \left({\mu }_{\text{k}}mg\right)=F\cos \theta \\ F=\left(\frac{{\mu }_{\text{k}}mg}{\cos \theta }\right)\end{array}$

By substituting the values of the variables in the above expression, the force required by the person to pull the object can be determined.

Hence, for the above-mentioned physical problem, the provided graph will be a part of the solution as it resembles the free body diagram of the situation and understand the forces acting on the object.