Crate being pulled with and without friction

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To solve the problem of a 51.0 kg crate being pulled with a constant force of 250 N across a frictionless surface followed by a surface with friction, the approach involves two segments. First, calculate the final velocity after the initial 10.0 m using Newton's second law, where the net force is solely 250 N. Then, for the next 10.0 m, account for friction by subtracting the frictional force from the applied force to determine the net force. Use the final velocity from the first segment as the initial velocity for the second segment and apply kinematics to find the final speed after the entire 20.0 m. This method effectively combines both parts of the motion to arrive at the final speed of the crate.
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Homework Statement



A 51.0 kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 250 N. For the first 10.0 m the floor is frictionless, and for the next 10.0 m the coefficient of friction is 0.20.

What is the final speed of the crate after being pulled these 20.0 m?


The Attempt at a Solution


I'm just really not sure what to do or where to start on this problem. please help.thanks
 
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I'm not to sure about this but I think you can divide it into two parts first. Find the Vf of the first 10.0 m then use that as the Vi for the other 10.0 m with friction and find the Vf again. That should give you the answer I believe.
 
Last edited:
Use Newton's 2nd law and vector summation to find the acceleration of the crate for both parts. For the first part the net force is just 250n, and for the second part it is 250n - Friction. Then use kinematics.
 

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