Treasure Cart
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acceleration, displacement?
if someone could work these out with me that would be great, have many other problems similar to these I need to solve.
1. Suppose you’re coding a game with a top-down view, and the player needs to push a cart full of treasure back to home base. The cart is sitting still, and it weighs 50lbs. If the player pushes with a constant force of 160N @ -35*, and the coefficient of kinetic friction is 0.2, what’s the cart’s acceleration?
2. If the player in the question above pushes the cart with a constant force for 5 seconds, what’s the carts displacement?
I assume 35* means 35 degrees with the surface. Then the parallel force is 160*cos(35). Also I will solve the problem with the mass expressed in kilograms as m.
Let g be the gravitational constant in terms of m/s^2. Then the vertical force is m*g+160*sin(35). The second term is the vertical component of the force applied externally. Thus the friction force is 0.2*(m*g+160*sin(35)).
The net force on the mass is
F=160*cos(35)-0.2*(m*g+160*sin(35))
If this is greater than zero, the mass moves, otherwise it stays still. If it moves, the acceleration is a=F/m.
The displacement is 0.5*a*t^2=0.5*a*25 where a is computed above.
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