- #1
VinnieD
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Homework Statement
There is no friction between any surfaces mass is known. Find acceleration of the blocks.
Homework Equations
F=ma
The Attempt at a Solution
I'm almost certian
Amx=g sin θ
AMy=0
Yes, these look correct.VinnieD said:Amx=g sin θ
AMy=0
That would be true if the wedge were fixed. But imagine if the wedge were not only frictionless but extremely light. The block would be almost in free fall.VinnieD said:Amx=g sin θ
For the block, the x direction is parallel to the incline. So, free fall acceleration would have an x-component of magnitude g sinθ.haruspex said:That would be true if the wedge were fixed. But imagine if the wedge were not only frictionless but extremely light. The block would be almost in free fall.
I had not picked up that x was defined as parallel to the slope.TSny said:For the block, the x direction is parallel to the incline. So, free fall acceleration would have an x-component of magnitude g sinθ.
Nor had I, especially since x is specifically drawn in his solution diagram as being the normal horizontal axisharuspex said:I had not picked up that x was defined as parallel to the slope.
The acceleration of a frictionless block on a frictionless 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. In this case, the only force acting on the block is gravity, which can be resolved into two components: perpendicular to the wedge's surface and parallel to the wedge's surface. The perpendicular component does not contribute to the block's acceleration, while the parallel component does. Therefore, the acceleration of the block is equal to the parallel component of gravity divided by the block's mass.
The angle of the wedge does not affect the acceleration of the block, as long as the wedge and block remain frictionless. This is because the only force acting on the block is gravity, which is always perpendicular to the wedge's surface. Therefore, the acceleration of the block will remain constant regardless of the angle of the wedge.
If friction is added to either the block or the wedge, it will affect the block's acceleration. Friction is a force that opposes motion, so it will act in the opposite direction of the block's motion. This means that it will reduce the acceleration of the block. The exact amount of reduction will depend on the coefficient of friction between the surfaces and the force of gravity acting on the block.
No, the acceleration of the block cannot be greater than the acceleration of gravity. This is because gravity is the only force acting on the block and it always acts in the direction of acceleration. The acceleration of the block can only be equal to or less than the acceleration of gravity.
The mass of the block does not affect its acceleration on a frictionless wedge. This is because acceleration is directly proportional to force and inversely proportional to mass. In this scenario, the only force acting on the block is gravity, which is constant. Therefore, the mass of the block will cancel out in the calculation of acceleration, and the acceleration will remain the same regardless of the block's mass.