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what would happen to the acceleration and velocity of the marble if the ramp were steeper

asked in Physics by anonymous


1 Answer

If you increase the steepness of the ramp, then you will increase the acceleration of a marble which rolls down the ramp. This can be seen in two different ways: 
 
1) Components of forces. Forces are vectors and have a direction and a magnitude. The force of gravity points straight down, but a marble rolling down a ramp doesn't go straight down, it follows the ramp. Therefore, only the component of the gravitational force which points along the direction of the marble's motion can accelerate the marble. The other component pushes the marble into the ramp, and the ramp pushes back, so there is no acceleration of the marble into the ramp. If the ramp is horizontal, then the marble does not accelerate, as gravity pushes the marble into the ramp and not along the surface of the ramp. If the ramp is vertical, the marble just drops with acceleration due to gravity. These arguments are changed a bit by the fact that the marble is rolling and not sliding, but that only affects the magnitude of the acceleration but not the fact that it increases with ramp steepness. 
 
2) Work and energy. The change in potential energy of the marble is its mass times the change in height (only the vertical component counts -- horizontal displacements do not change gravitational potential energy) times the local gravitational acceleration g. This loss of gravitational potential energy shows up as an increase in kinetic energy. If the marble falls a farther distance vertically, it will have a greater kinetic energy and be going faster. Again, the kinetic energy is shared between the motion of the marble going somewhere, and the rotation of the marble, but the dependence on the steepness of the ramp is the same.
answered by anonymous
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