Math Problem Statement
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.
Solution
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:
-
Gravitational force (Weight of the couch): This force acts downward and is given by , where:
- (mass of the couch)
- (acceleration due to gravity)
-
Normal force ( ): 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 will be equal to the gravitational force.
Calculation:
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:
- How does the angle of the applied force affect the normal force?
- What happens to the normal force if the couch is on an inclined plane?
- How would the normal force change if the couch were being pushed at an angle above the horizontal?
- What is the relationship between the normal force and frictional force?
- 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.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Newtonian Mechanics
Force Equilibrium
Formulas
Normal force F_N = m * g
Theorems
Newton's First Law
Suitable Grade Level
Grades 9-12
Related Recommendation
Calculate Weight and Normal Force for 1.008 kg Object
Calculating Weight and Normal Force for Stacked Boxes
Finding Normal Force on a Block with Two Applied Forces
Find Normal Force, Acceleration, and Net Force for a 60 N Applied Force with Friction
Find the Normal Force on an 8-kg Crate Pulled with a 50-N Applied Force