Dynamics

 Inclined Plane with Friction

 Whiteboard

 There is a 40kg crate sitting at the bottom of a ramp. The ramp is inclined at 25 degrees to the horizontal. An enterprising physics student needs to get the crate to the top of the incline. She devises a method where she attaches a rope to a crate, passes the rope over a pully and attaches the rope to a hanging mass. She is going to let the hanging mass pull the crate up the ramp for her! Here is some additional information: the coefficient of kinetic friction between the ramp and the crate is 0.45 and the hanging mass is 55kg. )The rope is massless and the pulley frisctionless, ah the wonders of technology!) We are going to begin our discussion the instant the crate begins to move. Q1: Draw a free body diagrm for both masses, label all forces. 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. Q5: What is the acceleration of the system? What would it mean if your acceleration were negative? 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? 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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