Question

Finding tension and acceleration of a connected blocks system?

Answer 1

If gravity's acceleration=20, and there's no friction, how could the acceleration of the system, plus the tension on each string, be calculated?

Answer 2

there's only 1 degree of freedom here. it is a 1-D problem.

plus there is no friction, so it is conservative.

i'd start with that and then use Conservation of Energy.

have you had a go, or are you required to fumble through FBD's?

Answer 3

Wouldn't that simply drag in v and h and other irrelevant variables?

Answer 4

I'm not understanding how if there isn't friction, then wouldn't acceleration be 20?

Answer 5

have you actually done this?! how did you do it?

Answer 6

I'm pretty stuck...

Answer 7

OK

here's a real cheat's way of doing this

the thing that is being accelerated has mass \(m_1 + m_2 + m_3\)

and the accelerating force is \(F = m_3 g = (m_1 + m_2 + m_3) a\)

so \(a = g\dfrac{m_3}{m_1 + m_2 + m_3}\)

you'll learn nothing from that, though.

draw a diagram and try some FBD is best way

Answer 8

Oh, I see. But what's the formula for tension? I'm getting inconsistent formulas for it.

Answer 9

Is T3=g*m3-(m1+m2)a?

Answer 10

i'd run with \(T_3 - m_3 g = (m_1 + m_2 + m_3) a\)

Answer 11

If you understand how to treat it as a system, as Irish showed, that's an easy way to find acceleration.

But you still need to draw FBD's for each object if you need to find the tensions in the ropes.

There is no "formula" for tension. Tension is just a force. Draw a free body diagram on each object; find the net force, and use it to find tension.

Answer 12

@IrishBoy123 shouldn't it be \[\large m_3 g - T_ 3 = m_3 a \]I'm making the positive direction downward