Mechanics: Dynamics (Newton's 2nd law)

[Oblivion77]

Homework Statement

A sphere S with a mass of 5 kg is attached by a rigid rod to 1 kg block B which is free to slide with no friction in a horizontal slot. The system is released from rest. At the instant when it is released, find the tension in the rod and the accelerations of both blocks.

Homework Equations

Sum of the forces in x = ma
Sum of the forces in y = ma

The Attempt at a Solution

I am not exactly sure how to tackle this problem. Would I need to solve this using Newton's 2nd law? Or would this question require conservation of energy? Thanks.

 

[Oblivion77]

Sorry wrong section

 

[fantispug]

Well if you were to use conservation of energy, how would you relate the energy to the tension in the rod and the accelerations of the blocks?

 

[Oblivion77]

Well if you were to use conservation of energy, how would you relate the energy to the tension in the rod and the accelerations of the blocks?

That's true, I have another question then. Since the problem is asking "the instant it is released from rest" can you assume the velocity is 0 at that instant? Therefore the component of normal acceleration is 0?

 

[fantispug]

Yeah, the velocity must be 0 at that instant (since it's at rest). But that can't possibly tell you anything about the acceleration at that instant; it's only if you knew the velocity at different times that you can use the velocity to find the acceleration.
(Consider the example of a pendulum; at the apex of the pendulum's swing the velocity of the pendulum is instantaneously zero, but it must be accelerating because the velocity increases a moment later as it starts swinging again).

You're going to have to crank out Newton's 2nd law I'm afraid.

 

[Oblivion77]

Yeah, the velocity must be 0 at that instant (since it's at rest). But that can't possibly tell you anything about the acceleration at that instant; it's only if you knew the velocity at different times that you can use the velocity to find the acceleration.
(Consider the example of a pendulum; at the apex of the pendulum's swing the velocity of the pendulum is instantaneously zero, but it must be accelerating because the velocity increases a moment later as it starts swinging again).

You're going to have to crank out Newton's 2nd law I'm afraid.

I understand that I need to use Newton's 2nd law, but I am confused on the swinging of the pendulum. Plus it looks like I would need to take relative accelerations into account. Since the swinging of the sphere is moving with the block.

 

[coltin.walsh]

you don't need to worry about the pendulum effect, or relative accelerations, since it asks for the accelerations at the instant it is released. You know the normal acceleration of the sphere is 0, since V=0 at the instant it is released. Solve for tangential acceleration, and tensions, the acceleration of block b