# Homework Help: HELPHow is this possible? The hanging mass is lighter then the cart!

1. Apr 8, 2013

### 13physicsdude

HELPHow is this possible?!? The hanging mass is lighter then the cart!

1. The problem statement, all variables and given/known data
The cart in Figure 4 has a mass of 2.3 kg and is attached to a 1.7 kg object. Calculate the acceleration of the cart given the following assumptions.

A) The force of friction is negligible

B) The frictional force acting on the wheels of the cart has a magnitude of 0.6 N.

C) Explain why the hanging mass does not accelerate downward at 9.8 m/s2

**btw Figure 4 simply shows a cart with wheels sitting on a horizontal surface with a string attached to the front, running from the front of the cart through a single pulley system at the corner of the table with a hanging mass attached to the end of the string, hanging off the table.

3. The attempt at a solution

A)

m1:
Fnet=T
ma=T
T=2.3a

m2:
Fg=mg
mg-t=ma
(1.7)(9.8)-T=1.7a

m1+m2:
16.66-2.3a=1.7a
16.66=4a
∴ a=4.165 m/s2

B)

m1:
T-Ff=ma
T-0.6=2.3a

m2:
Fg-t=ma
1.7g-t=1.7a

m1+m2:
1.7g-0.6=4a
16.66-0.6=4a
a=16.66-0.6/4
a=4.015 m/s2

C)

The reason the hanging mass does not accelerate downwards at 9.8 m/s2 is simply because gravity is not the only force acting on the hanging object. Tension of the rope is also a force acting on the object and is counteracting the effect of gravity just not at the same magnitude, thats why it still accelerates downward just not at 9.8 m/s2
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Apr 8, 2013

### haruspex

I'm not entirely sure what you're asking of the forum. From the title, you seem to be surprised that the cart moves at all. Is that the case?
I really don't like the wording in B. Wheels are designed to roll, not slide. Ignoring the moment of inertia of the wheels (since you have no data on that), the friction between the wheels and the table is irrelevant. So I assume this is referring to axle friction, but it should make that clear.
Your answer for C is ok, but perhaps they are looking for something which takes in the whole set-up rather than concentrating on the hanging mass. Maybe "the gravitational force on the hanging mass has to accelerate more than just its own mass".

3. Apr 9, 2013

### 13physicsdude

im asking if my answer is correct... and in the title i'm expressing that the question doesn't seem to make much sense

4. Apr 9, 2013

### haruspex

Your answers look fine. Why do you think the question doesn't make sense?