Homework Help: Hard Physics Problem on Forces

1. Oct 20, 2012

asheik234

1. The problem statement, all variables and given/known data
An airplane begins its takeoff sequence moving with a constant acceleration a. A passenger holds up a pocketwatch during the takeoff sequence and notices that the watch makes an angle θ = 14° with the vertical, and that 13.3 seconds pass before the plane leaves the runway.

(a) What is the plane's constant acceleration?

(b) How far does the plane travel on the runway?

2. Relevant equations

F = ma

3. The attempt at a solution

There is no given mass, I don't know how to find it without it.

2. Oct 20, 2012

Staff: Mentor

Just call the mass 'm'. You won't need the actual value.

3. Oct 20, 2012

asheik234

can you explain how?

4. Oct 20, 2012

Staff: Mentor

Apply Newton's 2nd law. What forces act on the pocketwatch? Analyze horizontal and vertical force components separately.

5. Oct 20, 2012

asheik234

I tried but still nothing, the vertical component is mg and the horizontal one is 9.5m(mg*cos14), am I missing something?

6. Oct 20, 2012

Staff: Mentor

First things first. What forces act on the watch? (There are two forces acting: Name them.)

7. Oct 20, 2012

asheik234

Force tension and force weight

8. Oct 20, 2012

Staff: Mentor

Excellent. What are the horizontal and vertical components of each force? (The weight is mg; call the tension force "T".)

9. Oct 20, 2012

asheik234

Components of force weight:
horizontal component: 0
vertical component: mg

Components of force tension:
horizontal component: mg*cos14
vertical component: mg

10. Oct 20, 2012

Staff: Mentor

Good. (The vertical component acts down.)

No. (The vertical component will end up equal to mg, but you'll get to that in the next step.)

The tension force is T. It acts parallel to the chain of the watch. What are its components?

11. Oct 20, 2012

asheik234

horizontal component: T * sin14
vertical component: mg

12. Oct 21, 2012

Staff: Mentor

Good.

But I would have preferred:
Horizontal: T*sin14
Vertical: T*cos14

Nice and simple.

Now apply ƩF = ma to the vertical and horizontal components.