Can you help me draw the free body diagram and help me solve this problem thanks

Question

Can you help me draw the free body diagram and help me solve this problem thanks!
Book: physics for scientists and engineers a strategic approach 3rd edition Good Luck . IN ORDER TO RECEIVE CREDIT FOR THIS PROBLEM YOU MUST solve DIAGRAM/Equations table format. MAKE SURE THAT YOUR DIAGR THIS PROBLEM YOU MUST solve it in the Given/To Be Determined GRAM/Equations table format. MAKE SURE THAT YOUR DIAGRAM IS CONSISTENT WITH YOUR GIVEN. TBD AND EQUATIONS. Circle your final answers. A ball of mass m moves down a smooth incline with an initial speed vo starting at a travels as shown below. Use energy methods to answer the following questions. height h above the horizontal surface and Give all answers in terms of m, g. va h, d k and Ha NOTE: Do not use the picture above for the diagraml.YoOU MUST DRAW YOUR not use the picture above for the diagram!·YOU MUST DRAW YOUR OwN DIAGRAM a) What is the speed of the ball when it reaches the bottom of the incline? (10 points) b) If the spring shown in the problem has a constant k, then what is the maximum compression of the spring if the horizontal surface is frictionless? (10 points) c) If the horizontal surface contains a rough distance d maximum compression of the spring in this case? (10 points) zontal surface contains a rough distance d which is characterized by a coefficient of friction s, then what is the

Explanation / Answer

Ans (a) At the bottom whole of potential energy of ball is converted into kinetic energy

m*vo^2/2=mgh

vo=(2gh)^0.5

(b) if the horizontal surface is frictionless then whole kinetic energy of ball is converted into elastic energy of spring

k*x^2/2=m*vo^2/2

x^2=m*2*g*h/k

therefore maximum compression of spring=x=(19.62*m*h/k)

(c) if a frictional surface of distance d exists then

elastic energy of spring=kinetic energy of ball-friction work

k*x^2/2=m*vo^2/2-uk*m*g*d

k*x^2/2=m*g*h-uk*m*g*d

x^2=19.61*m(h-uk*d)

x=(19.61*m(h-uk*d))^0.5

x=4.43(m(h-uk*d))^0.5

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