Small block with velocity inside a large block at rest

In summary, the problem involves the conservation of linear momentum and energy in a system consisting of two blocks on a frictionless surface. The blocks are not an isolated system due to external forces, including a normal force in the y-direction. The momentum is not conserved in the x-direction due to these external forces.
  • #1
CoconutFred
3
1

Homework Statement



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Homework Equations



(Conservation of momentum)
(Conservation of energy)

The Attempt at a Solution



I know linear momentum must be conserved on the X-axis, so

mvo=mv1x+Mv2

where v1 is the final velocity of the small mass and v2 is the final velocity of the large mass. Also, M=2m.

Energy is also conserved, so

(1/2)mvo2=(1/2)mv12+(1/2)Mv22+mgR

Since the problem stipulates that the 2 blocks never lose contact with each other, I'm guessing the momentum in the x direction would actually be

mvo=(m+M)v2

and v2=v1x

But I'm not sure if that is right, and so I'm not totally sure where to go from here.
 
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  • #2
It looks like you have all the physics in place to solve it. Keep going with the algebra ...

When I solved it I wrote everything in terms of the velocity ##\vec{v}## of the small block, so that

##v^{\ 2}=v_x^{\ 2}+v_y^{\ 2}.##
 
Last edited:
  • #3
I don't think that momentum is conserved in the x-direction.
What can one say about conservation of momentum in the y-direction?
Also, the two blocks do not form an isolated system because of the normal
force on the larger block by the frictionless surface.
 
  • #4
J Hann said:
I don't think that momentum is conserved in the x-direction.
What can one say about conservation of momentum in the y-direction?

There are no external forces in the x-direction.
There are external forces in the y-direction.

Also, the two blocks do not form an isolated system because of the normal
force on the larger block by the frictionless surface.

That normal force is one of the external forces in the y-direction.
 

FAQ: Small block with velocity inside a large block at rest

What is the concept of a small block with velocity inside a large block at rest?

The concept of a small block with velocity inside a large block at rest refers to a system where a smaller object, such as a ball, is moving inside a larger object, such as a box, which is not moving or at rest. This creates a scenario where the smaller object is in motion relative to the larger object, but both objects are in the same reference frame.

What factors affect the velocity of the small block inside the large block?

The velocity of the small block inside the large block can be affected by factors such as the initial velocity of the small block, the mass and size of both objects, and any external forces acting on the system, such as friction or air resistance. The velocity of the small block can also change due to collisions or interactions with the walls of the larger block.

How does the velocity of the small block inside the large block change over time?

The velocity of the small block inside the large block can change over time due to various forces and collisions. In a closed system with no external forces, the velocity of the small block will remain constant due to the law of conservation of momentum. However, if there are external forces or collisions, the velocity of the small block may increase, decrease, or change direction.

Can the small block inside the large block ever have a higher velocity than the initial velocity of the small block?

Yes, it is possible for the small block inside the large block to have a higher velocity than its initial velocity. This can occur if the small block experiences a series of collisions or interactions with the walls of the larger block, causing its velocity to increase. However, this increase in velocity is limited by factors such as the mass and size of the objects and the strength of the collisions or forces.

What are some real-life examples of a small block with velocity inside a large block at rest?

One example of a small block with velocity inside a large block at rest is a ball bouncing inside a moving train. Another example is a car moving inside a larger truck. Both scenarios involve a smaller object in motion relative to a larger object that is not moving or at rest. These examples demonstrate the concept of relative motion and the effects of collisions and forces on the velocity of the smaller object.

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