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

In summary: So in summary, the cart would go up 7.7m if launched from the spring with an initial velocity of 12.3m/s.
  • #1
zan123_
7
0
New user has been reminded to always show their work on schoolwork problems.
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
javalab20230725073519.png
 
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  • #2
zan123_ said:
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?
 
  • #3
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
 
  • #4
zan123_ said:
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.
 
  • #5
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
 
  • #6
zan123_ said:
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.
 
Last edited:
  • #7
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
 
  • #8
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.
 
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  • #9
kuruman said:
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.
 
  • #10
jbriggs444 said:
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
kuruman said:
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.
 

1. How does a cart launched by a spring slide up a ramp?

When a cart is launched by a spring, it is given a certain amount of potential energy. As the cart moves up the ramp, this potential energy is converted into kinetic energy. The ramp provides an inclined surface for the cart to move along, reducing the amount of force needed to move the cart upwards.

2. What is the role of the spring in this experiment?

The spring in this experiment acts as a source of potential energy. When the spring is compressed, it stores potential energy which is then released to launch the cart. The spring also helps to provide a consistent and controlled force to the cart, ensuring that the experiment can be repeated accurately.

3. How does the angle of the ramp affect the motion of the cart?

The angle of the ramp affects the motion of the cart by changing the amount of force required to move the cart up the ramp. A steeper ramp will require more force to overcome gravity and move the cart upwards, while a shallower ramp will require less force. The angle also affects the speed and acceleration of the cart as it moves up the ramp.

4. What factors can affect the accuracy of the results in this experiment?

There are several factors that can affect the accuracy of the results in this experiment. These include the precision of the equipment used, the angle and surface of the ramp, air resistance, and any external forces acting on the cart. It is important to control these variables as much as possible in order to obtain accurate and reliable results.

5. How can this experiment be applied in real-life situations?

This experiment can be applied in real-life situations to study the principles of energy and motion. It can also be used to understand the concept of potential and kinetic energy, as well as the effects of inclined surfaces on the motion of objects. This experiment can also be used to design and test different types of ramps for practical applications, such as wheelchair ramps or ski jumps.

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