# Find the force needed for a body on an inclined plane to be static?

• Like Tony Stark
In summary: Therefore, the acceleration calculated using Newton's equations is with respect to the inertial frame of reference, which in this case would be Earth.
Like Tony Stark
Homework Statement
The picture shows a body of mass ##m_1## lying on an inclined surface of mass ##m_2##. Suppose that all surfaces are frictionless. Determine the horizontal accelaration that sould be applied to ##m_2## to keep ##m_1## in equilibrium. Then, suppose that an acceleration twice bigger than the calculated previously is applied to ##m_2##, what's the acceleration of ##m_1## with respect to Earth (inertial system) and with respect to ##m_2##?
Relevant Equations
Newton's equations
Here, I have two doubts
1) if the surfaces are frictionless, then there's no force being applied on the ##x' axis## of ##m_1## except from the weight, so it should be sliding, shouldn't it? So, there's no force that I could apply to ##m_2## to keep ##m_1## in equilibrium since any force that I apply on ##m_2## will manifest in the normal force of ##m_1## and this is on the ##y'## axis of ##m_1##.

2) And then I have some problems with "acceleration with respect to...". If I use Newton's equations and I solve for ##a##, that acceleration is with respect to ##m_2## or with respect to Earth?

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• 20190927_131007.jpg
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Like Tony Stark said:
Here, I have two doubts
1) if the surfaces are frictionless, then there's no force being applied on the ##x' axis## of ##m_1## except from the weight, so it should be sliding, shouldn't it? So, there's no force that I could apply to ##m_2## to keep ##m_1## in equilibrium since any force that I apply on ##m_2## will manifest in the normal force of ##m_1## and this is on the ##y'## axis of ##m_1##.

Your doubts shouldn't stop you doing the calculations.

Like Tony Stark said:
2) And then I have some problems with "acceleration with respect to...". If I use Newton's equations and I solve for ##a##, that acceleration is with respect to ##m_2## or with respect to Earth?

Newton's laws apply in an inertial reference frame.

Last edited:

## 1. What is the formula for calculating the force needed for a body on an inclined plane to be static?

The formula for calculating the force needed for a body on an inclined plane to be static is F = mg sinθ, where F is the force, m is the mass of the body, g is the acceleration due to gravity, and θ is the angle of the inclined plane.

## 2. How does the angle of the inclined plane affect the force needed for a body to be static?

The force needed for a body to be static on an inclined plane increases as the angle of the inclined plane increases. This is because the component of the gravitational force acting parallel to the inclined plane also increases with the angle, making it harder for the body to stay in place.

## 3. Can the force needed for a body to be static on an inclined plane be greater than its weight?

Yes, the force needed for a body to be static on an inclined plane can be greater than its weight. This can happen when the angle of the inclined plane is steep enough, causing the component of the gravitational force acting parallel to the inclined plane to exceed the weight of the body.

## 4. What other factors can affect the force needed for a body to be static on an inclined plane?

The force needed for a body to be static on an inclined plane can also be affected by the coefficient of friction between the body and the inclined plane, the shape and size of the body, and any external forces acting on the body.

## 5. Is the force needed for a body to be static on an inclined plane constant?

No, the force needed for a body to be static on an inclined plane is not constant. It varies depending on the angle of the inclined plane and other factors such as the coefficient of friction and external forces. It is only constant when all these factors remain constant.

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