# Can you figure this out?

1. Jan 5, 2005

### Stargate

Can you figure this out!?

Suppose that a cart is being moved by a certain net force. If the net force is doubled, by how much does the acceleration change? Why does this happen? For what reason?

2. Jan 5, 2005

### dextercioby

Given the second law
$$F=ma$$
and taking into account that mass wouldn't change,what do you think it will happen to the acceleration?

Daniel.

3. Jan 5, 2005

### quasar987

The "rigorous" proof should follow from an analysis of the equations $F_1=ma_1$ and $F_2=ma_2$. What is $a_2$ in terms of $a_1$ if you set $F_2=2F_1$?

4. Jan 5, 2005

### Stargate

The acceleration slows, right? Why does this happen?

5. Jan 5, 2005

### dextercioby

Because the two forces are applied on the same body (which means the same mass) and the second force is twice as big as the first,i'd say the acceleration doubles...
Wouldn't u agree??

Daniel.

6. Jan 5, 2005

### Stargate

I have no idea what you are talking about quasar! Could you explain?

7. Jan 5, 2005

### Stargate

I do agree thanks! Any you explain quasar987 reply?

8. Jan 5, 2005

### dextercioby

Let's say u have a body of mass "m".U apply a force on it.Call it "F".The second law of dynamics says that the acceleration imprimed by this force (call it "a") is nothing but
$$a=\frac{F}{m}$$

Now apply the force doubled.Which means the force 2F.Call the new acceleration "a'" ("a" prime)?Again,the second law says that the acceleration is the ratio between force and mass
$$a'=\frac{2F}{m}=2\frac{F}{m}=2a$$
,where u made use of the first formula to express the new acceleration in terms of the old one.
Therefore,the acceleration doubles.

Daniel.

9. Jan 5, 2005

### Stargate

I get it now! thank you for your help!