Forces Acting on Mass M on Wedge

In summary, the conversation discusses a body of mass M on a sledge with a coefficient of friction between the wedge and sledge of μ and an angle of α. The sledge is pushed with an initial velocity and the forces acting on the plates at the sides of the sledge are calculated using Newton's Second Law. The resultant force is determined to be -mgμ*cosα pointing up the slope.
  • #1
Gloyn
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Homework Statement


We have a body of mass M placed in a kind of sledge like on the picture:
imgJPG_xsrqhxq.JPG


Coefficient of fristion between the mass and the sledge is zero, but the coefficient of friction between the wedge and the sledge is μ. Angle of the wedge is α. The sledge is massles. The slegde is pushed with some initial velocity up the wedge. What are the forces that the mass M acts with on the plates at the sides of the sledge?

Homework Equations



Inertial force: F_I=-ma
2nd Newten s Law F=ma

The Attempt at a Solution



If the sledge was not moving, the force acting on the left plate would be F=mg*sinα, but since it is moving, we calculate the acceleration down the wedge, which is:

ma=mg*sinα+mgμ*cosα -> a= g(sinα+μ*cosα)

So the resultant force is:

F=mg*sinα-(mg*sinα+mgμ*cosα)=-mgμ*cosα

and it points up the wedge. Is that right?
 
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  • #2
I sort of agree with you but would quibble over the wording.

The resultant force is always given by ma.

When going up the slope a=g(sinα+μ*cosα)
But when going down a=g(sinα-μ*cosα)
Resultant F=ma=mg*sinα+ reaction force from plates.
Reaction force from plates=±mgμ*cosα
So when going up the slope the mass is pushing on the plate to the right in your diagram, but when sliding down pushes on the left hand plate.
 
  • #3
You're right of course :) Thanks for help!
 

FAQ: Forces Acting on Mass M on Wedge

What is the definition of "Forces Acting on Mass M on Wedge"?

Forces Acting on Mass M on Wedge refers to the physical forces that act on an object with mass M that is placed on a wedge inclined at an angle. These forces can include gravity, normal force, friction, and applied forces.

What is the relationship between the angle of the wedge and the forces acting on Mass M?

The angle of the wedge directly affects the magnitude and direction of the forces acting on Mass M. As the angle increases, the force of gravity pulling the mass down the wedge increases, while the normal force acting perpendicular to the wedge decreases. Friction also increases with a steeper angle, making it harder for the mass to slide down the wedge.

How do the forces acting on Mass M on Wedge affect its motion?

The forces acting on Mass M on Wedge determine its acceleration and direction of motion. If the net force is positive, the mass will accelerate down the wedge. If the net force is negative, the mass will decelerate or move in the opposite direction. The angle of the wedge also affects the motion, with steeper angles resulting in slower or more difficult motion.

What is the role of friction in the forces acting on Mass M on Wedge?

Friction is a force that acts in the opposite direction of motion and can make it more difficult for Mass M to move down the wedge. The coefficient of friction, which depends on the materials and surface of the wedge and mass, determines the strength of the frictional force. In some cases, friction can be helpful in keeping the mass in place on the wedge.

How can the forces acting on Mass M on Wedge be calculated and analyzed?

The forces acting on Mass M on Wedge can be calculated using Newton's Second Law, which states that the net force on an object is equal to its mass multiplied by its acceleration. By analyzing the individual forces (gravity, normal force, friction, and applied forces) and their directions and magnitudes, the overall motion and behavior of Mass M on Wedge can be predicted and understood.

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