Cart and ramp with same mass(dynamics)

  • Thread starter masacre
  • Start date
  • Tags
    Cart Ramp
In summary, the conversation discusses the problem of finding the speed and distance of a cart rolling on a ramp with no friction, air resistance, or moment of inertia. The solution involves using the principle of conservation of energy and momentum to find the initial speed of the cart and the speed of the ramp when the cart rolls off. The final step is to calculate the horizontal projection range and subtract the distance the ramp moved during the cart's free fall.
  • #1
masacre
4
0

Homework Statement


On flat surface there is small cart m and big, initally resting ramp with mass m and height h.
a) At what speed should the cart travel to roll on the flat area on top of the ramp and stop relativly to it?
b) Assuming that cart moves with speed greater than calculated in a) what is the distance d between it and ramp when the it hits the ground?

Friction, air resistance and moment of inertia of the wheels of ramp and cart are neglible. Cart does not detach from ramp during rolling.

Image:
Bez_tytu_u.png


Homework Equations


The Attempt at a Solution


a)
I wanted to use the principle of conservation of energy and came up with equation like this:
[itex]mv^{2}/2=2mv_{0}^{2}/2 + mgh[/itex]
Where v is initial speed of cart (what I need to find knowing only m,h and g) and [itex]v_{0}[/itex] is speed of ramp and cart on it after the cart finish its movment in relation to ramp.
I know I need a second equation here but I can't find it. I was trying to find this equation using principle of conservation of momentum but I am not sure wheter the momentum is same on the beginning and at the end of movement.
b)
Here I need to know what is the speed of the ramp after the cart 'jumps' of it, then I know how to calculate the distance when I know it. But still I need help with finding out the speed of the ramp.
 
Last edited:
Physics news on Phys.org
  • #2
masacre said:
I know I need a second equation here but I can't find it. I was trying to find this equation using principle of conservation of momentum but I am not sure whether the momentum is same on the beginning and at the end of movement.
Since there are no horizontal forces between the cart+ramp system and anything external to it (such as the ground), horizontal momentum is conserved.
 
  • #3
So my second equation is:

[itex]mv=2mv_{0} [/itex]

and the solution for a) therefore is:

[itex] v = 2√{gh} [/itex]

But what concerns me isn't there a normal(normal to ramp) force acting on cart when it rolls, which might has horizontal component because ramp is at some angle to surface.
 
  • #4
masacre said:
what concerns me isn't there a normal(normal to ramp) force acting on cart when it rolls, which might has horizontal component because ramp is at some angle to surface.
You are told that when the cart reaches the flat portion at top of ramp the cart and ramp happen to be at the same speed. That will be a consequence of the horizontal force between cart and ramp during ascent being 'just right'. You don't even know whether the ramp is a straight line or a curve - and you don't need to. In short, you only care about the consequence of that horizontal force, not its details.
 
  • #5
Alright, so for b) I have these two equations to solve for [itex]v_{r}[/itex](ramp speed) and[itex]v_{c}[/itex](cart speed):
[itex]mv^2/2=mv_{r}^{2}/2+mv_{c}^{2}/2+mgh[/itex]
[itex]mv=mv_{c}+m_{r}[/itex]

And then I only have to calculate horizontal projection range and substract distance ramp moved during cart's free fall?
 
  • #6
masacre said:
Alright, so for b) I have these two equations to solve for [itex]v_{r}[/itex](ramp speed) and[itex]v_{c}[/itex](cart speed):
[itex]mv^2/2=mv_{r}^{2}/2+mv_{c}^{2}/2+mgh[/itex]
[itex]mv=mv_{c}+mv_{r}[/itex]

And then I only have to calculate horizontal projection range and substract distance ramp moved during cart's free fall?
Yes.
 

1. What is the relationship between the cart and ramp in this scenario?

The cart and ramp have the same mass, which means they have equal amounts of matter. This also means that they have the same weight, or force of gravity acting on them. In this scenario, the cart is placed on the ramp and they will both move together.

2. How does the mass of the cart affect its movement on the ramp?

The mass of the cart affects its movement on the ramp because it determines the amount of force needed to move the cart. The greater the mass, the more force is needed to move the cart up the ramp. This is due to the principle of inertia, which states that objects with more mass require more force to move.

3. What is the role of gravity in this scenario?

Gravity plays a crucial role in this scenario as it is the force that pulls the cart and ramp down towards the ground. The force of gravity is dependent on the mass of the objects, so in this case, the cart and ramp have the same weight due to their equal mass. Gravity causes the cart to move down the ramp.

4. How does the angle of the ramp affect the movement of the cart?

The angle of the ramp affects the movement of the cart because it determines the slope or incline of the ramp. The steeper the angle, the more force is needed to push the cart up the ramp. This is because the steeper angle increases the component of gravity that pulls the cart down the ramp, making it harder to move against it.

5. What other factors may affect the movement of the cart on the ramp?

Aside from mass and angle, other factors that may affect the movement of the cart on the ramp include friction and air resistance. Friction is the force that opposes the movement of the cart on the surface of the ramp, and air resistance is the force that resists the motion of the cart as it moves through the air. These forces can slow down the cart and affect its acceleration on the ramp.

Similar threads

  • Introductory Physics Homework Help
Replies
18
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
13
Views
836
  • Introductory Physics Homework Help
Replies
15
Views
1K
  • Introductory Physics Homework Help
2
Replies
40
Views
2K
  • Introductory Physics Homework Help
Replies
32
Views
2K
  • Introductory Physics Homework Help
2
Replies
56
Views
1K
  • Introductory Physics Homework Help
Replies
24
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
993
  • Introductory Physics Homework Help
Replies
2
Views
3K
Back
Top