Chapter 5.2, Problem 32SSC

To determine

The force that accelerates the dresser.

To Explain: The circumstances under which the dresser can slide and the direction of sliding of the dresser.

Explanation of Solution

Introduction:

When an object is placed on sloping surface and is at rest,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.

Newton’s Second Law:

The object’s acceleration is equivalent to the sum of the forces acting on the object divided by the object’s mass. That is,

$\begin{array}{l}a=\frac{F_{\text{net}}}{m}\\ F_{\text{net}}=ma\end{array}$

Here, $m$ is the mass and $a$ is the acceleration of the object.

Consider a person R is moving to a new apartment and places the dresser in the back of a pickup truck.

When the truck is not moving, the dresser will also be in rest and the static frictional force exists in the contact surface between the dresser and the truck.

When the truck is accelerated in the forward direction,

According to Newton’s Second Law of Motion, a force is exerted on the dresser. When the force’s magnitude is more than the static frictional force existing between the contact surface of the dresser and the truck, the dresser will move in the backward direction and kinetic friction comes into action at the contact surface.

Hence, when the force (produced due to the acceleration of the truck) exceeds the static frictional force existing in the contact surface between the dresser and truck, the truck will slide in the opposite direction of motion of truck.

Conclusion:

Thus, when the force (produced due to the acceleration of the truck) exceeds the static frictional force existing in the contact surface between the dresser and truck, the truck will slide in the opposite direction of motion of truck.