Ramps - Study Guides

The basis for ramp problems is the same for ALL of our forces problems:

  • If an object experiences unbalanced forces in the "x" or "horizontal" direction, it will accelerate in the direction of the unbalanced force.

  • If an object experiences unbalanced forces in the "y" or " vertical" direction, it will accelerate in the direction of the unbalanced force.

  • If an object is at rest in the "x" or "horizontal" direction the forces in that direction MUST be balanced or absent.

  • If an object is at rest in the "y" or "vertical" direction the forces in that direction MUST be balanced or absent.

THE VERY BIG difference in RAMP problems is that we tilt the Universe and the "x" direction becomes "Down the Ramp" while the "y" direction becomes "Perpindicular to the Ramp" or NORMAL to the ramp.

Also, there is ONE and ONLY one force that is responsible for every aspect of our conversations of ramps.... weight (mg)

As always, we mathematically we express those situations as:

∑Fx = max

∑Fy= may

 

THEREFORE--

Our job is to

(1) determine if the forces acting in the horizontal ("x") direction are balanced or unbalanced

(2) verify that the forces acting in the vertical ("y") direction are balanced and can therefore be ignored.

 

TO WIT:

RAMP PROBLEMS REVIEW

As noted above, the weight of an object posed to slide down a ramp is the entire source of all the forces present that we'll discuss when working on ramp problems.

  • The force pulling the object down the ramp in the "x" dimension is NOT simply the weight of the force. It is the weight of the force in the "x" direction:

mgsinΘ

  • The frictional force is generated in preportion to the Normal force of the weight (mg) of the object. The deciding factor here is the frictional coefficient μ:

f = μN

Since the Normal force itself is dependent on the weight (mg) of the object, we can express friction in terms of the weight of the object by substituting for N as follows:

f = μmgcosΘ

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Now that is all well and good... IF you know how to get the x and y components of the objects weight (mg).

  • The first step is to sketch and label the object on the ramp with the weight (mg) vector pointing stright down to the center of the Earth.

  • Next, sketch the Normal force of the ramp pushing up on the box perpindicular to the surface of the ramp

  • The Normal force is resisted by the (y) component of the the weight (mg) of the object, so sketch that next. Label that mgcosΘ

  • The last step is connect your two vectors with a vector that is paralell to the direction of the ramp itself. That is the component of the force pulling the object down the ramp. Label that mgsinΘ

 

If Fx (the force down the ramp) is greater than f (friction) then the object will slide. If they are equal, it won't. Also, the frictional force can NEVER be larger than Fx

A worked solution is here:

A basic, intermediate and difficult ramp problems are found HERE

Worked Problems:

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HOMEWORK: 

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