Intro Physics -- Cart launched by a spring slides up a ramp...

[zan123_]

Homework Statement

The cart is set up with a frictionless apparatus as shown in the figure below. If the cart launched from the spring has an initial velocity of 12.3m/s how high up the ramp would it go? Show your work.

Relevant Equations

The mass of the cart is 5 kg. The ramp is 4 m. Pls let me know if you need more info

 

[Chestermiller]

Homework Statement: The cart is set up with a frictionless apparatus as shown in the figure below. If the cart launched from the spring has an initial velocity of 12.3m/s how high up the ramp would it go? Show your work.
Relevant Equations: The mass of the cart is 5 kg. The ramp is 4 m. Pls let me know if you need more info

View attachment 329629

What is your assessment so far?

 

[zan123_]

could you clarify what do you mean? it is on a 5 kg cart moving down a 4 m ramp. i don't know what equations i should use to calculate this

 

[haruspex]

could you clarify what do you mean? it is on a 5 kg cart moving down a 4 m ramp. i don't know what equations i should use to calculate this

What standard equations or conservation laws have you been taught that might relate to this?
On this forum, you are required to show some attempt.

 

[zan123_]

oh okay, i have learned equations but i have a hard time applying them in word questions like these. we dont have a lot of problems to practise so i've been having trouble. Since I have the velocity would i do:

Ek=1/2mv^2
= 1/2(5)(12.3)^2
Ek=378.225 J

Eg=mgh
=(5)(9.8)(4)
196 J

Emech=ek+eg
=574.225 J

i honestly dont know how to find the distance

 

[kuruman]

i honestly dont know how to find the distance

Consider the following:
What is the velocity of the cart when it is at the distance you're looking for?
Play a movie in your head that shows the motion of the cart from the moment it starts moving until it reaches the required distance. Then think how this motion could be related to the equations you posted in #5.

 

[zan123_]

does this work?

vf^2=vi^2 + 2ad
0 = 12.3^2 +2(9.8)d
0 = 151.29 + 19.6d
d = 15129/19.6
d=7.7 m

 

[kuruman]

It doesn't work because it assumes that the acceleration of the cart is the acceleration of gravity, i.e. that the cart is in free fall which it isn't.

 

[jbriggs444]

It doesn't work because it assumes that the acceleration of the cart is the acceleration of gravity, i.e. that the cart is in free fall which it isn't.

However, the approach only needs a tiny bit of additional reasoning in order to become correct. Something about how potential energy is independent of the path.

 

[kuruman]

However, the approach only needs a tiny bit of additional reasoning in order to become correct. Something about how potential energy is independent of the path.

I think the additional reasoning should also include the answer to my question

What is the velocity of the cart when it is at the distance you're looking for?

the significance of which I am not convinced that OP understands.