# Physics. Three masses on friction less surface?

There is no friction anywhere. The cart system is let go with everything initially at rest. Find accelerations for each of the three masses relative to the ground. (They are all different.) I am absolutely stump on this one anyone want to give it a try ?

### 2 Answers

- NCSLv 75 years agoFavorite Answer
I think it works something like this.

Horizontally blocks 2 and 3 behave as one.

Let's say that block 3 accelerates downward at "a".

a = g*m3 / (m2 + m3)

Horizontally, the CM must remain stationary, so

a*m1 = a' * (m2 + m3)

where a' is the acceleration (to the left) of m2 and m3.

Substituting for "a" on the LHS we have

g*m3*m1 / (m2 + m3) = a' * (m2 + m3)

a' = g * m1 * m3 / (m2 + m3)²

Conclusions:

m2 accelerates horizontally to the left at a' = g * m1 * m3 / (m2 + m3)²

m1 accelerates at horizontally to the right at

a = g*m3 / (m2 + m3)

m3 has vertical acceleration "a" AND horizontal acceleration a', so its acceleration is

√(a'² + a²) = g * (m3 / (m2 + m3))√(1 + m1² / (m2 + m3)²)

Maybe.

EDIT: I originally had a different answer, and I'm starting to like it better.

Conclusions:

m2 accelerates to the left as above.

m1 accelerates at horizontally to the right at

a - a' = g * (m3 / (m2 + m3) - m1*m3 / (m2 + m3)²), or

a - a' = g*(m3 / (m2 + m3))(1 - m1/(m2 + m3))

(I'm troubled by this, though, since a negative number will result if m1 is larger than m2+m3.)

m3 has vertical acceleration "a" AND horizontal acceleration a', so its acceleration is

√(a'² + (a - a')²)

You can substitute for a and a' if you like; too much for me to type here.

If you find this helpful, please award Best Answer!

- electron1Lv 75 years ago
The only force is the weight of block 3. Since block is moving downward, its weight will not affect the acceleration of the cart.

Weight = m * 9.8

To determine the acceleration of blocks 1and 2, divide by 2 m

a = m * 9.8 ÷ 2 m = 4.9 m/s^2

This is the acceleration of the two blocks. The acceleration of 3 is 0 m/s^2.

But doesn't the question say that each mass has a different acceleration?