What is the acceleration of the wedge on a slope with a block on top?

In summary, the system consists of a wedge with mass M and a block with mass m on top, with no friction between them. When the system is released from rest, the wedge will experience an acceleration due to the reaction force from the block. This force has a horizontal component, which can be calculated by multiplying the normal force on the block (n) by the cosine of the angle of inclination (alpha). The acceleration of the wedge can then be determined by using Newton's second law (F=ma).
  • #1
Pixter
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A wedge with mass M rests on a fricitonsless horizontal table top. a block with mass m is placed on the wedge. There is no friction between the block and the wedge. The system is released from rest.

q1: calculate the accelration of the wedge

now why would the wedge have any accelration at all? wouldn't just stand still?..

I can't get how I'm suppose to calculate the acceleration of the wedge.
 
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  • #2
The wedge exerts a reaction force on the thing on the wedge. From Newton's third law there must consequently be a force on the wedge equal to the normal reaction force. As this force is not perpendicular to the horizontal a component of this force is in the horizontal direction, producing an accelleration on the wedge.
 
  • #3
So if the normal force for the block is n the opposite one which is the one that acts on the wedge will be m*g*cos(aplha).. but how do I get the horizontel component for this force?
 

What is a block on slope?

A block on slope refers to a block or object that is resting or sliding on an inclined surface. It is a common problem in mechanics that involves studying the forces and motion of the block on the slope.

What factors affect the motion of a block on slope?

The motion of a block on slope is affected by several factors, including the mass of the block, the angle of the slope, the coefficient of friction between the block and the slope, and the applied external forces.

How do you calculate the forces acting on a block on slope?

To calculate the forces acting on a block on slope, one must first draw a free body diagram of the block and identify all the forces acting on it, including the weight, normal force, frictional force, and any external forces. Then, using Newton's second law of motion, the net force and resulting acceleration can be determined.

What is the role of friction in a block on slope?

Friction plays a crucial role in the motion of a block on slope. It is the force that opposes the motion of the block and is responsible for keeping the block from sliding down the slope. The amount of friction present depends on the coefficient of friction between the block and the slope surface.

How does the angle of the slope affect the motion of a block on slope?

The angle of the slope has a significant impact on the motion of a block on slope. As the angle of the slope increases, the force of gravity pulling the block down the slope also increases, making it more challenging for the block to stay in place. This results in a greater frictional force and a slower motion of the block. On the other hand, a lower angle of slope will result in a smaller frictional force and a faster motion of the block.

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