Sliding mass on sliding incline

In summary, the question asks for the acceleration of the mass M on a frictionless incline, and the attempted solution involves finding the horizontal force and using it to calculate the acceleration. However, the correct solution involves considering the forces on both blocks and using the equation F(net)=ma. It is important to consider the direction of the accelerations as well.
  • #1
zheng89120
149
0

Homework Statement



A block of mass m slides down the incline of a triangular block of mass M. The angle of inclination is [tex]\theta[/tex]. The trianguilar block is free to slide on a horizontal plane. Assume that all surfaces are frictionless. What is the acceleration of the mass M?

Homework Equations



F(net)=ma=0

The Attempt at a Solution



so basically i want to ask if my answer is correct, as I'm not familiar with this type of problem, i got:

F(horizontal) = mg cos [tex]\theta[/tex] sin [tex]\theta[/tex]
a(M, horizontal) = F(horizontal) / (m + M)

is this right?
 
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  • #2
zheng89120 said:

Homework Statement



A block of mass m slides down the incline of a triangular block of mass M. The angle of inclination is [tex]\theta[/tex]. The trianguilar block is free to slide on a horizontal plane. Assume that all surfaces are frictionless. What is the acceleration of the mass M?

Homework Equations



F(net)=ma=0

The Attempt at a Solution



so basically i want to ask if my answer is correct, as I'm not familiar with this type of problem, i got:

F(horizontal) = mg cos [tex]\theta[/tex] sin [tex]\theta[/tex]
a(M, horizontal) = F(horizontal) / (m + M)

is this right?
Not quite. Are the accelerations of the 2 blocks the same? What about the direction of the accelerations?
 

FAQ: Sliding mass on sliding incline

How does the mass of the object affect its acceleration down the incline?

The mass of the object does not affect its acceleration down the incline. According to the law of gravity, all objects experience the same acceleration due to gravity regardless of their mass. However, the mass of the object does affect the force of friction acting against it, which can impact its acceleration.

What factors influence the speed at which the mass slides down the incline?

The speed at which the mass slides down the incline is influenced by several factors, including the angle of the incline, the force of gravity, the coefficient of friction, and the mass of the object. The steeper the incline, the greater the acceleration due to gravity, and the lower the friction, the faster the mass will slide down the incline.

Can the angle of the incline affect the direction of the force of gravity?

No, the angle of the incline does not affect the direction of the force of gravity. The force of gravity always acts directly downwards towards the center of the Earth, regardless of the angle of the incline.

How does the coefficient of friction impact the movement of the mass on the incline?

The coefficient of friction is a measure of the amount of resistance between two surfaces. A higher coefficient of friction means there is more resistance, which will slow down the movement of the mass on the incline. A lower coefficient of friction means there is less resistance, allowing the mass to move more quickly down the incline.

Is the motion of the mass on the incline affected by air resistance?

Yes, air resistance can impact the motion of the mass on the incline. However, the effect of air resistance is typically very small and can be ignored in most cases when calculating the movement of the mass. Air resistance becomes more significant when the mass is moving at higher speeds or over longer distances.

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