Normal forces on inclined plane

In summary, the conversation discusses a problem involving a 1.0 kg box on a 30 degree frictionless incline connected to a 3.0 kg box on a horizontal frictionless surface through a frictionless and massless pulley. The forces and equations for both boxes are discussed, including the normal force, tension, and weight. It is suggested to draw two free body diagrams and use trigonometry to resolve the weight vector into x-y components.
  • #1
GingerBread27
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A 1.0 kg box on a 30 degree frictionless incline is connected to a 3.0 kg box on a horizontal frictionless
surface. The pulley is frictionless and massless.

I got n=mg for m1 in the y direction, and in the x direction i got F+T=m1a. For m2 in the y direction i get N-m2gcos(theta)=0, and in the x direction i get m2gsin(theta)-T=m2a. Is this correct?
 

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  • #2
Start with the box on an inclined plane, the gravity pulls down and the slope pushes perpendicularly to itself, then the normal force for the second box on the flat plane is mg the tension actually makes no difference to the normal force. If you are looking for all the forces then the tension is the horizontal component of the first normal force
 
  • #3
You should have two FBD's for this problem. It makes things a lot easier IMO. Draw A fbw for both boxes as if they are on a flat surface. Draw one box with a tension force to the right (top box) and the other with a tension force to the left (bottom box). Here's the tricky part--the weight of the inclined box does not act normal to the surface of the plane (normal means 90 degrees btw or perpendicular). How many degrees is the weight of the box from the normal direction of the inclined box? Next, if I told you the weigh of the inclined box was the hypotenuse of a triangle would that help you resolve the weight vector into x-y vectors (hint hint).

good luck.
 

FAQ: Normal forces on inclined plane

What is a normal force on an inclined plane?

The normal force on an inclined plane is a force that is perpendicular to the surface of the plane. It is also known as the support force, and it prevents objects from falling through the surface of the inclined plane.

How is the normal force on an inclined plane calculated?

The normal force on an inclined plane can be calculated using the formula FN = mg cosθ, where FN is the normal force, m is the mass of the object, g is the acceleration due to gravity, and θ is the angle of inclination.

Does the normal force on an inclined plane always equal the weight of the object?

No, the normal force on an inclined plane is only equal to the weight of the object if the angle of inclination is 0°. As the angle increases, the normal force decreases and the component of the weight parallel to the plane increases.

Can the normal force on an inclined plane be greater than the weight of the object?

Yes, the normal force on an inclined plane can be greater than the weight of the object if the angle of inclination is less than 90°. In this case, the normal force will be larger to counteract the component of the weight parallel to the plane.

How does friction affect the normal force on an inclined plane?

Friction can decrease the normal force on an inclined plane. As the object slides down the plane, the frictional force acting against it will reduce the overall normal force. However, if the object is at rest or moving up the inclined plane, friction will increase the normal force.

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