Math

Question5. Figure 7 shows a fan cart. \square (a) Explain why the fan cart cannot accelerate. (b) Explain why the fan cart can accelerate if the rigid sail is removed. sail \square Figure 7

Studdy Solution

STEP 1

What is this asking? Why does a fan cart with a sail attached not move, but *does* move if you take the sail away? Watch out! Don't forget Newton's **Third Law**: for every action, there's an equal and opposite reaction!

STEP 2

1. Analyze the forces with the sail.
2. Analyze the forces without the sail.

STEP 3

Alright, picture this: we've got our fan cart, ready to roll!
The fan is *blowing* air backwards onto the sail.
This creates a **force**!

STEP 4

Now, here's the kicker: that sail is *rigidly* attached to the cart.
So, that force from the fan blowing on the sail is also pushing on the *cart* itself, trying to move it forward.
Let's call this force FfanF_{\text{fan}}.

STEP 5

But wait!
Newton's **Third Law** jumps in!
The air hitting the sail pushes *back* on the fan with an equal and opposite force.
Since the fan and sail are connected, this force, Ffan -F_{\text{fan}} , acts on the cart too!

STEP 6

So, what's the *total* force on the cart?
It's the force from the fan pushing forward *plus* the force from the sail pushing backward: Ffan+(Ffan)=0 F_{\text{fan}} + (-F_{\text{fan}}) = 0 .
Zero force means **no acceleration**!
The forces are balanced!

STEP 7

Now, imagine we take the sail away. *Whoosh!* The fan blows air backwards, and *that's* our action.

STEP 8

The reaction?
The air pushes *forward* on the fan!
Let's call this force Fair F_{\text{air}} .
Since there's no sail to get in the way, this force is acting directly on the cart.

STEP 9

Is there a force pushing backward this time?
Nope! The air is free to move behind the cart.
So, the *total* force on the cart is just Fair F_{\text{air}} , which is *not* zero.

STEP 10

A net force that isn't zero means **acceleration**!
The cart *moves*!

STEP 11

(a) The fan cart cannot accelerate with the sail because the force of the fan on the sail (and thus the cart) is canceled out by the equal and opposite force of the sail on the fan (also acting on the cart).
(b) Removing the sail allows the fan to push air backward, and the reaction force of the air on the fan propels the cart forward.
No balancing force exists in this case, so the cart accelerates!

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