Can you find the Force without acceleration?

[xZerocopyx]

Homework Statement

In 1453, during the siege of Constantinople, the Turks used a cannon capable of launching a stone cannonball with a mass of 5.40 X 10^2. Suppose a soldier dropped a cannonball with this mass while trying to load it into the cannon. The cannonball rolled down a hill that made an angle of 30 degrees with the horizontal. If 5.20 X 10^4 J of work was done by gravity on the cannonball on the cannonball as it rolled down a hill, how far did it roll?

Homework Equations

W=Fdcos(30)

The Attempt at a Solution

d=W/Fcos(30)
F=ma
d=W/macos(30)
d=(5300)/(540)acos(30)

What am I doing wrong?

 

[cubejunkies]

Draw a free body diagram. What forces are acting on the cannonball as it rolls down the hill?

 

[xZerocopyx]

I can't really draw on the screen but I can say it. The forces acting I guess are Fg(force of gravity)(down), the Fn (Normal force)(up) and the force of the ball Rolling downhill?(east)

 

[Pengwuino]

You're making this much too difficult. Imagine a triangle making an angle 30 degrees off the horizontal. What does conservation of energy tell you about how much vertical distance is covered if a certain amount of energy is given to the object?

 

[xZerocopyx]

I don't know. Al we learned so far is the Conservation of Mechanical Energy, which is MEi =MEf, but to use this seems extremely complicated, unless I am misunderstanding it...

 

[Pengwuino]

I don't know. Al we learned so far is the Conservation of Mechanical Energy, which is MEi =MEf, but to use this seems extremely complicated, unless I am misunderstanding it...

Conservation of energy is the simplest thing in the world! The energy a system is always conserved. The amount of energy gained by moving an object in a gravitational field in this situation is simply $$\delta PE = mg\delta h$$where m is the mass, g is the acceleration of gravity, and $$\delta h$$ is the distance the object is moved. So if an object has had a certain energy put into it by a gravitational field (and you assume the object doesn't have any kinetic energy before and after), then you can tell how far it fell. Then it comes down to simple trigonometry.

 

[cubejunkies]

If the only force acting on the object is the force of gravity, you can use g as the acceleration

 

[xZerocopyx]

Ok. thanks