Answer :
To find the frictional force between the table and the floor, we first need to determine whether the table is stationary or in motion. Since the table is stationary, we will consider static friction.
Step-by-step Explanation:
Understand Static Friction:
- Static friction acts on objects that are not moving, to prevent their movement.
- It can vary up to a maximum value, which depends on the normal (perpendicular) force and the coefficient of static friction.
Calculate the Normal Force:
- The normal force is the force exerted by a surface to support the weight of an object resting on it. For an object on a horizontal surface, this equals the gravitational force.
- The weight of the table can be calculated as:
[tex]\text{Weight} = m \times g[/tex] - Where:
- [tex]m = 103 \text{ kg}[/tex] is the mass of the table,
- [tex]g = 9.81 \text{ m/s}^2[/tex] is the acceleration due to gravity.
- Thus, the weight (normal force) is:
[tex]103 \times 9.81 = 1010.43 \text{ N}[/tex]
Determine the Maximum Static Frictional Force:
- The maximum static friction force can be calculated using:
[tex]F_{\text{static max}} = \mu_s \times F_{\text{normal}}[/tex] - Where:
- [tex]\mu_s = 0.87[/tex] is the coefficient of static friction,
- [tex]F_{\text{normal}} = 1010.43 \text{ N}[/tex] is the normal force.
- Substituting the values, we find:
[tex]F_{\text{static max}} = 0.87 \times 1010.43 = 878.0751 \text{ N}[/tex] - Thus, the frictional force acting on the stationary table is [tex]878.0751 \text{ N}[/tex].
- The maximum static friction force can be calculated using:
In summary, because the table is not moving, the frictional force is equal to the maximum static frictional force, which is approximately [tex]878.08 \text{ N}[/tex].
