Inclined Slope Problem

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  • #1
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If I pull a box at a small horizontal angle (say 5 degrees) with a constant force up the slope, and pull another box with the same magnitude of force (at say 60 degrees) up, will the two boxes have the same acceleration, or will one box accelerate faster? If so, which one is accelerating faster? This is a frictionless system.

I can't decide if this is a trick question or not.

Can I set a = F / (m * sin(theta)) with fake numbers? In that case, the angle with the smallest degree will have the highest acceleration, but is this correct?
 

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  • #2
Fermat
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Newton's law, F=ma, shows you that the accln of an object, in a particlular direction, is directly proportional to the (net) force acting on the object (in that direction).
Since the object is only moving up the slope, the largest force up the slope will produce the largest accln.

In other words yes, you're right !!
 
  • #3
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Draw out the free-body diagrams on the box. Mainly, there are 2 forces, one would be the pulling force while the other, will be the weight on the box. Break up the components of the weight and you will see that there is this artificial friction on the box caused by the horizontal component of the weight. Since the pulling force on both blocks are the same, u can compare the artificial friction to see which friction is the larger one and that will be the one with a smaller resultant force and a smaller acceleration. Basically, since the weight of the block in both cases is a constant, the one that has a lower incline will result in a smaller angle of artificial friction created. Hence, the acceleration of that block will be faster.

Well.. provided no explanation is required, you know, common sense do tell u that the incline that has a smaller angle will have a larger acceleration.
 
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