What Is the Plane's Constant Acceleration During Takeoff?

[asheik234]

1. Homework Statement
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. Homework Equations

F = ma

3. The Attempt at a Solution

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

 

[Doc Al]

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

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

 

[asheik234]

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

can you explain how?

 

[Doc Al]

can you explain how?

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

 

[asheik234]

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

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

 

[Doc Al]

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

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

 

[asheik234]

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

Force tension and force weight

 

[Doc Al]

Force tension and force weight

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

 

[asheik234]

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

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

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

 

[Doc Al]

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

Good. (The vertical component acts down.)

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

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?

 

[asheik234]

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?

horizontal component: T * sin14
vertical component: mg

 

[Doc Al]

horizontal component: T * sin14
vertical component: mg

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.