Object sliding down horizontal, frictionless slope, crossing horizontal surface

[kapowa]

Homework Statement

block A slides down an 8 m frictionless ramp that is curved 30 degrees above the horizontal.
it then crosses a 4m surface that has a coefficient of friction that is 0.20.
it then hits a ball and continues moving at 3 m/s.

the ball is suspended from a string, kinda like a pendulum. You have to find out how high the ball goes.

mass of block a is 5kg
mass of ball a is 2.5 kg

Homework Equations

Ek = 0.5mv^2
Eg = mgh
vf^2 = vi^2 + 2ad
Ff= μFn
p=mv

The Attempt at a Solution

to find the speed of the block after sliding down the ramp, i simply used some the sin function to determine the vertical distance the block moved down the ramp and then used the formula E(gravity)= mgh to find out the energy it had at the top of the ramp. I then converted this energy to kinetic energy (formula E(kinetic) = 0.5mv^2) which it would have gained at the bottom of the ramp and found the speed to be around 8.85 m/s.

then to find the speed after the block crossed the 4m distance, i used the the formula for friction. To find the normal force, i used Fg = mg because gravity and normal force are the same in magnitude, and put this in the F(friction) = μFn formula and then got the negative acceleration and plugged that into the kinematics formula above to get a speed of about 7.9 m/s after crossing the 4m surface.

then i used momentum to figure out the height of the ball in the pendulum. Before the collision the momentum was mass of block (5 kg) times speed (abt 7.9 m/s). I setup the formula for the collison like this

momentum before = 5kg x (approx. 7.9m/s)

after the collision the block was moving at 3 m/s
momentum after = 5 kg x (3 m/s) + 2.5(v(of ball a))

since momentum is conserved i solved the equation to find v of ball a which was about 9 m/s. i then used the kinetic energy formula to find the energy at that point right after the collision. At this point kinetic energy was at a max and potential energy was at a minimum. I then converted the energy to potential which would have happened when the pendulum swung to one side. I used the formula Ep = mgh to finally find the height of the ball which i got to be around 5meters (4.9 something)

I am not sure if this was correct way of doing it. I saw a similar question elsewhere and saw that the answers were somewhat different. i wanted to know if i was right in the way i did it, the asnwer did seem reasonable to me.

 

[technician]

I have not checked any of your maths calculation but I cannot find anything wrong with your method

 

[kapowa]

I have not checked any of your maths calculation but I cannot find anything wrong with your method

Okay, thanks a lot. I just wanted to know if my reasoning was correct. The numbers don't really matter that much. It was just a practice question.

 

[ehild]

It looks correct. But keep at least 3 significant digits in the intermediate results .

ehild

 

[asteriatic]

Your approach seems correct and your answer is reasonable. However, it is always a good idea to double check your calculations and make sure you are using the correct equations and values. It is also important to clearly state your assumptions and show all your work to ensure a complete and accurate solution. Additionally, it may be helpful to provide diagrams or illustrations to aid in the understanding of your solution. Overall, your response shows a good understanding of the concepts and equations involved in solving this problem.