The above picture shows a force diagram for someone pushing a couch at a constant speed across a floor to the right using an applied force of 89 N. The couch has a mass of 157.8 kg. How much is the normal force (FFl on C) to the nearest 0.1 N? Do not include units.



To calculate the normal force acting on the couch, we need to consider the forces acting in the vertical direction. Since the couch is being pushed across the floor at a constant speed, it means that the vertical forces are in equilibrium (i.e., the sum of the vertical forces equals zero).

### Forces acting on the couch:
1. **Gravitational force (Weight of the couch)**: This force acts downward and is given by \( F_g = m \cdot g \), where:
   - \( m = 157.8 \, \text{kg} \) (mass of the couch)
   - \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)

2. **Normal force ( \( F_{N} \) )**: This force acts upward and balances the gravitational force.

Since the person is pushing the couch horizontally, the applied force does not affect the vertical forces. Therefore, the normal force \( F_{N} \) will be equal to the gravitational force.

### Calculation:
\[
F_{N} = F_g = m \cdot g = 157.8 \, \text{kg} \times 9.8 \, \text{m/s}^2
\]

Let's compute this.The normal force acting on the couch is approximately **1546.4** (to the nearest 0.1 N).

Do you want more details or have any questions?

Here are some related questions:
1. How does the angle of the applied force affect the normal force?
2. What happens to the normal force if the couch is on an inclined plane?
3. How would the normal force change if the couch were being pushed at an angle above the horizontal?
4. What is the relationship between the normal force and frictional force?
5. How does increasing the mass of the couch affect the normal force?

**Tip:** Remember that the normal force is always perpendicular to the surface and counteracts the weight of the object on that surface.

The above picture shows a force diagram for someone pushing a couch at a constant speed across a floor to the right using an applied force of 89 N. The couch has a mass of 157.8 kg. How much is the normal force (FFl on C) to the nearest 0.1 N? Do not include units.

Learn how to calculate the normal force acting on a couch with a mass of 157.8 kg being pushed at a constant speed. This problem involves concepts from Newtonian mechanics, including force equilibrium and the application of the formula F_N = m * g. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation