Force applied to a mass of an inclined plane with mass

In summary: Now, in terms of forces, the only force acting in the x direction is the force of gravity. And in the y direction, we have the normal force and the force of gravity.So, in summary, the force applied on the little mass is equal to the force of gravity in the x direction, which is -mgsinθ, and in the y direction, it is equal to the normal force, which is +mg, and the sum of these two forces will equal to zero in the y direction since there is no acceleration in that direction. Therefore, the force applied on the little mass is F=-mgsinθ+Mgsinθ. Your mistake was in considering the normal force as the only force acting on the
  • #1
JordanGo
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There is a box of mass m on a wedge of mass M with angle θ (the triangle also has a angle of 90 degrees). I need to find the force applied on the little mass, this is what I got:
F=-mgsinθ+Mgsinθ
Where the first term refers to the force of gravity applied to the mass m and the second term refers to the normal force applied on m by M.
I think my mistake is the normal force because looking at the limits when M is really big, the mass m moves in the opposite direction that gravity pushes it.

Can someone help me set this force up?

P.S. the surface of the wedge is frictionless and the surface in which the wedge lies on is frictionless.
 
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  • #2
your mistake is that the normal force acting on the box should be equal and opposite to the force acting on it that is perpendicular to the surface that it's resting on

look at a simple example: box sitting on the ground, no angles

there is the force of gravity acting on this box, which is -mg

the normal force therefore is equal and opposite to the force of gravity, which in this case is also perpendicular to the surface

so the normal force acting on this block is +mgan important thing to remember is that if an object is not moving or has a constant velocity, then the sum of the forces acting on that object need to equal zero.

This also applies for each component of the force. What that means is that if the box is not accelerating in the x direction, then the forces in the x direction must add up to be zero. And the same thing in the case of the y direction.
So, if we look at your example, we see a block on a wedge. Sometimes it helps to think about things in terms of common sense: if you put a block on a wedge, what would happen to the block. Obviously it would slide down the wedge.

So let's say that the y direction is perpendicular to the surface of the wedge, and the x direction is parallel to the surface of the wedge. And by surface I mean the surface on which the block is sitting.

If we think about it this way, we can see that there will be no acceleration in the y direction, but there will be acceleration in the x direction. There's no acceleration in the y direction because... well it's not like the block is going to fly off the wedge or fly "into" the wedge, that would make no sense.

Therefore, the forces in the y direction need to add up to zero.

But the forces in the x direction should *not* add up to zero.
 

Related to Force applied to a mass of an inclined plane with mass

What is the formula for calculating the force applied to a mass on an inclined plane?

The formula for calculating the force applied to a mass on an inclined plane is F = mgsinθ, where F is the force applied, m is the mass of the object, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of inclination of the plane.

How does the mass of an object affect the force needed to move it on an inclined plane?

The mass of an object does not directly affect the force needed to move it on an inclined plane. However, the weight (mg) of the object does play a role in determining the force needed, along with the angle of inclination and the force of friction.

What is the relationship between the angle of inclination and the force needed to move an object on an inclined plane?

The force needed to move an object on an inclined plane increases as the angle of inclination increases. This is because as the angle increases, the component of the weight of the object acting parallel to the plane also increases, requiring a greater force to overcome it.

How does the force of friction affect the movement of an object on an inclined plane?

The force of friction acts in the opposite direction of motion, making it harder for the object to move on the inclined plane. It increases with the weight of the object and the roughness of the surface, and decreases as the angle of inclination increases. The net force needed to move the object is the difference between the applied force and the force of friction.

What are some real-life applications of the concept of force applied to a mass on an inclined plane?

This concept is commonly used in the construction industry to determine the force needed to move materials up ramps or inclined surfaces. It is also used in transportation, such as calculating the force needed to move a train up a hill or to launch a rocket into space. Additionally, understanding this concept is crucial in sports, such as skiing or snowboarding, where the angle of the slope and force applied can affect the speed of the athlete.

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