Dynamics

 Inclined Plane with Friction

 Solutions

Q1: Draw a free body diagrm for both masses, label all forces.  Mass 1 Mass 2

Q2: Assuming the +x-hat axis is up the incline, write an equation that shows the sum of all forces in the x direction. For example, SFx and the sum of all forces in the y direction, SFy for M1. Q3: Do the same thing for M2, assume that y-hat is vertical. Q4: Look at the equation you derived for question #2 above. How many forces are you assuming in the x direction? How many in the y direction? Can we ignore any of these forces? If so, which ones and why.

Looking at problem #2, there are three forces in the x direction and two forces in the y direction. The forces in the y direction are equal and opposite thus cancelling each other, therefore they do not effect the block's acceleration and can be ignored.

Q5: What is the acceleration of the system? What would it mean if your acceleration were negative? The acceleration is positive so the crate is moving up the incline. If the acceleration had been negitive the crate would be moving down the incline.

Q6: What is the tension of the rope? Q7: Let us assume that the ramp is 10 meters long (and that the crate slides the entire 10 meters). What is the speed of the crate when it gets to the top of the ramp?

Since the crate is accelerating up the 10 meter ramp, we can easily find the final velocity at the top of the ramp.

Q8: If our enterprising physics student stops the crate in 1.5 seconds, then how much force does she apply to the crate?

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