Magnitude of Normal Force (Frictionless)

In summary, to solve for the normal force exerted on the crate, one must analyze the vertical components of the forces acting on the crate. This includes gravity (9.8 m/s^2 downward), the normal force exerted by the crate itself, and the third vertical component (sin(23.5 degrees) x 100). By balancing these forces, the magnitude of the normal force can be determined to be 530N.
  • #1
Spartan Erik
31
0

Homework Statement



"A crate of mass 50 kg is pushed across a frictionless horizontal floor with a force of 100N directed 23.5 degrees below the horizontal. The magnitude of the normal force of the floor on the crate is:"

Homework Equations



F = ma? Not sure what else would apply.. mainly a conceptual issue here

The Attempt at a Solution



I took 100N x cos(23.5) in order to get the horizontal force which turns out to by 91.7N.. not sure what to do from here
 
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  • #2
To solve for the normal force, analyze the vertical components of the forces acting on the crate. (Three forces act.)
 
  • #3
Well gravity is acting on the crate (9.8 m/s^2 downward), and the crate itself has a normal force exerted in the opposite direction
 
  • #4
Gravity and the normal force are two of the three forces. What's the third vertical component?
 
  • #5
Well I imagine the third component could be sin(23.5 degrees) x 100 = 39.875
 
  • #6
Spartan Erik said:
Well I imagine the third component could be sin(23.5 degrees) x 100 = 39.875
Right. So what must the normal force be to balance this force plus gravity?
 
  • #7
Ah so 9.8 m/s^2 x 50kg = 490N

And adding that to 39.875N will result in a magnitude of 530N
 

Related to Magnitude of Normal Force (Frictionless)

1. What is the magnitude of normal force in a frictionless system?

The magnitude of normal force in a frictionless system is equal to the weight of the object. This is because in a frictionless system, there is no opposing force acting on the object, so the normal force must be equal to the weight of the object in order to maintain equilibrium.

2. How does the magnitude of normal force change in a frictionless system?

In a frictionless system, the magnitude of normal force remains constant throughout the motion. This is because there is no friction to change the normal force, so it will always be equal to the weight of the object.

3. Does the magnitude of normal force depend on the mass of the object?

Yes, the magnitude of normal force is directly proportional to the mass of the object. This means that as the mass of the object increases, the normal force also increases in order to maintain equilibrium.

4. How is the magnitude of normal force affected by the angle of the surface?

The magnitude of normal force is affected by the angle of the surface in a frictionless system. As the angle of the surface increases, the normal force decreases because some of the weight of the object is now acting in a direction perpendicular to the surface.

5. Can the magnitude of normal force be negative in a frictionless system?

No, the magnitude of normal force cannot be negative in a frictionless system. This is because the normal force is always acting perpendicular to the surface, so it cannot have a negative value. If there is an opposing force acting on the object, it would be considered a different type of force, such as a tension force or a gravitational force.

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