What is the speed of block one when block 2 has fallen h?

• Vitani11
In summary: The coefficient of static friction between block 1 and the table is μs and kinetic is μk.In summary, the equation states that the speed of block 1 is greater than the difference in the tension and static friction forces between block 1 and the table.
Vitani11

Homework Statement

A block with a mass m1 is held in place on a table and is attached to a block with mass m2 by a massless inextensible string that passes over a massless pulley with frictionless bearings. The coefficient of static friction between block 1 and the table is μs and kinetic is μk. When block 1 is released, what must be true for block 2 to fall? If that requirement is met, what is the speed of block 1 when block 2 has fallen a distance h?

Homework Equations

Conservation of energy
Ko +Uo -W = Kf + Uf

The Attempt at a Solution

In order for block 2 to fall its force due to tension and gravity has to be greater than the difference between the force of block one due to tension and its force of static friction. This is what I think. Thoughts? Also, how would I put this in terms of conservation of energy?

For the speed I used (1/2)(m1 +m2)V2km1gh = (1/2)(m1+m2)gh and solved for V. I used h for the part of work because the same distance block 2 falls is the distance block 1 moves.

Here is the set up. Because I defined the potential energy being 0 as the initial height of mass 2 I think there should be a potential on the left side of the equation, but then it would be negative.

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Vitani11 said:
In order for block 2 to fall its force due to tension and gravity has to be greater than the difference between the force of block one due to tension and its force of static friction.
That is not right. You might have confused yourself in the process of writing it out in words. Write it as an inequality in algebra.
Vitani11 said:
(1/2)(m1 +m2)V2 -μkm1gh = (1/2)(m1+m2)gh
No. According to that, the greater the friction, the greater the velocity.

Okay so if I changed the signs in the equation is it then valid? Or am I missing terms still?
And the total energy of block 2 has to be greater than the addition of kinetic energy and work rather than the difference between its force and friction. How is that?

Vitani11 said:
if I changed the signs in the equation is it then valid?
No. Explain the potential energy term.
Vitani11 said:
the total energy of block 2 has to be greater than the addition of kinetic energy and work rather than the difference between its force and friction.
For part 1? No. Take what you wrote initially and turn it into an algebraic inequality.

Vitani11
Wow holy cow I'm so sorry for that... I've got the right equation - thank you again for your help. I've written the inequality and saw what was not right.

What is the speed of block one when block 2 has fallen h?

The speed of block one when block 2 has fallen h is dependent on several factors such as the mass and height of the blocks, as well as the force of gravity. To determine the speed, we can use the equation v = √(2gh), where g is the acceleration due to gravity (9.8 m/s²) and h is the height fallen.

What is the acceleration of block one when block 2 has fallen h?

The acceleration of block one when block 2 has fallen h is equal to the acceleration due to gravity (g). This is a constant value of 9.8 m/s² and is not affected by the mass or height of the blocks.

How does the mass of block one affect its speed when block 2 has fallen h?

The mass of block one does not affect its speed when block 2 has fallen h. The speed is only determined by the height fallen and the acceleration due to gravity. The mass of the block will, however, affect the force of gravity acting on it.

Is the speed of block one the same as the speed of block 2 when block 2 has fallen h?

No, the speed of block one will not be the same as the speed of block 2 when block 2 has fallen h. This is because the blocks have different masses and will experience different forces of gravity. However, the speed of block one can be calculated using the same equation as block 2.

How does air resistance affect the speed of block one when block 2 has fallen h?

If air resistance is present, it will decrease the speed of block one when block 2 has fallen h. This is because the force of air resistance acts in the opposite direction of motion and will slow down the block. The extent to which air resistance affects the speed will depend on the surface area and shape of the block.

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