91Ó°ÊÓ

When an object, like the ice cart in this exercise, is placed on a horizontal surface, the force that acts perpendicularly to this surface is called the normal force. It is denoted by the symbol \( N \). For objects that are at rest and have no vertical acceleration, the normal force equals the gravitational force acting on the object.

To find the normal force, you consider the mass \( m \) of the object and multiply it by the acceleration due to gravity \( g \), giving you the equation:

• \( N = mg \)

For our ice cart of mass \( 60 \text{ kg} \) on a snow patch, this results in a normal force of \[ N = 60 \times 9.8 = 588 \text{ N} \]
This means the cart is exerting a force of 588 Newtons on the snow patch because of its weight.

The coefficient of friction is a measure that defines the frictional force between two surfaces. In this exercise, we are concerned with static friction, which prevents the object from moving. The coefficient of static friction is represented by \( \mu_s \).

It usually ranges between 0 and 1, where higher values indicate stronger friction between surfaces. In our case, the snow and the ice cart have a static friction coefficient \( \mu_s = \frac{1}{3} \).

This value is crucial for calculating the maximum static friction force. It acts as a multiplier of the normal force, helping us understand how resistant the object is to starting movement. The smaller the coefficient, the easier it is for the object to move.

The maximum static friction force is the force threshold that must be exceeded to make an object move. Before this threshold is reached, static friction acts to keep the object at rest.

The equation to calculate maximum static friction force is:

• \( f_s = \mu_s N \)

For the ice cart, with \( \mu_s = \frac{1}{3} \) and \( N = 588 \text{ N} \), the maximum static friction force calculates as:\[f_s = \frac{1}{3} \times 588 = 196 \text{ N}\]This result tells us that a horizontal force greater than 196 Newtons is needed to overcome static friction and move the ice cart. It's essentially the friction barrier that must be surpassed.