Answer :
To solve this problem, we need to calculate the normal force acting on a couch that is at rest on a horizontal surface. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, it's the force that the floor exerts on the couch.
Here's a step-by-step solution:
1. Identify the Forces:
- The primary force acting on the couch is its weight, which acts downward due to gravity.
- The normal force acts upward, balancing the weight of the couch because it is at rest on a horizontal surface.
2. Understand the Concept of Normal Force:
- On a flat surface, the normal force is equal to the gravitational force acting on the object. This is because there are no other vertical forces acting on the couch.
3. Calculate the Weight of the Couch:
- The weight ([tex]\( W \)[/tex]) of an object is calculated using the formula:
[tex]\[
W = m \times g
\][/tex]
where [tex]\( m \)[/tex] is the mass of the object in kilograms, and [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex].
4. Plug in the Values:
- For the couch, [tex]\( m = 124 \, \text{kg} \)[/tex] and [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex].
5. Calculation:
- [tex]\[
W = 124 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 1215.2 \, \text{N}
\][/tex]
6. Determine the Normal Force:
- Since the couch is at rest and there are no other vertical forces, the normal force ([tex]\( N \)[/tex]) is equal to the weight.
- So, [tex]\( N = 1215.2 \, \text{N} \)[/tex].
Therefore, the normal force acting on the couch is [tex]\( 1215.2 \, \text{N} \)[/tex].
Here's a step-by-step solution:
1. Identify the Forces:
- The primary force acting on the couch is its weight, which acts downward due to gravity.
- The normal force acts upward, balancing the weight of the couch because it is at rest on a horizontal surface.
2. Understand the Concept of Normal Force:
- On a flat surface, the normal force is equal to the gravitational force acting on the object. This is because there are no other vertical forces acting on the couch.
3. Calculate the Weight of the Couch:
- The weight ([tex]\( W \)[/tex]) of an object is calculated using the formula:
[tex]\[
W = m \times g
\][/tex]
where [tex]\( m \)[/tex] is the mass of the object in kilograms, and [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex].
4. Plug in the Values:
- For the couch, [tex]\( m = 124 \, \text{kg} \)[/tex] and [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex].
5. Calculation:
- [tex]\[
W = 124 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 1215.2 \, \text{N}
\][/tex]
6. Determine the Normal Force:
- Since the couch is at rest and there are no other vertical forces, the normal force ([tex]\( N \)[/tex]) is equal to the weight.
- So, [tex]\( N = 1215.2 \, \text{N} \)[/tex].
Therefore, the normal force acting on the couch is [tex]\( 1215.2 \, \text{N} \)[/tex].
