A spring with a spring constant, k = 500.0 N/m, is used to get a 0.500 kg mass up an incline. The spring is initially compressed 30.0 cm from equilibrium and launches the mass eastward along a horizontal surface onto the plane (the base of the incline is 1.50 m east of the front edge of the mass before the mass is released). The plane has a length of 4.00 m and makes an angle of 30.0° North of West with the horizontal. The coefficient of friction between the 0.500 kg mass and the horizontal surface, and the surface of the plane, is 0.350.
Determine:
a) The speed of the mass at the point it reaches the bottom of the inclined plane.
b) The speed of the mass at the point it reaches the top of the inclined plane (if it reaches the top and if it reaches the top with non-zero speed).
c) The total work done by friction if the block reaches the top of the incline with non-zero, "forward", speed.
d) Determine the maximum height, relative to the horizontal surface, it will reach if the block reaches the top with zero speed.
e) Determine the speed the block would initially require to give it a speed at the top of the incline that would allow it to reach a maximum height of 2.50 m.