6. A cart of mass 400 kg starts from rest at the top of a frictionless track as shown. At the end of the run there is a rough part of the track 10.0 m long that slows the cart down by friction (coefficient of kinetic friction 0.50). Everywhere else the track is frictionless. Just in case the cart is not completely stopped by friction, there is a spring just after the rough section as shown. Find the following: (a) What is the change in gravitational potential energy between the initial state (cart on top of hill) and when it comes to the rough section? (b) What is the speed of the cart just before it encounters the rough section of the track? (c) What is the speed of the cart just after it leaves the rough section of the track and before it hits the spring? (d) How far is the spring compressed if the spring constant is 1600 N/m? 21.0m 9.0m Rough section Spring 10m wwww