# Torques exerted by Gravity (CONFUSING)

1. Nov 6, 2008

### avenkat0

1. The problem statement, all variables and given/known data
A door with symmetry and of m 43.1 kg is 4.76 m high and 2.68 wide. The hinges are placed all the way on top and all the way on the bottom of the door. Find the absolute value of the horizontal force supplied by the bottom hinge.

2. Relevant equations
Sum of torques = 0
Torque = R x F

3. The attempt at a solution
I tried finding the torque exerted by gravity... and equaling that to the torque exerted by the hinges...
F(L)=W/2(mg)
now would i divide the force by 2 since there are 2 hinges?
or is my reasoning wrong from the first place?

2. Nov 6, 2008

3. Nov 6, 2008

### avenkat0

Ohh ok i did exactly that and it came out to be wrong...
119.026 came out to be my answer...

4. Nov 7, 2008

### Staff: Mentor

That answer seems about right to me. (Is this one of those on-line homework systems?)

5. Nov 7, 2008

### avenkat0

Yeah its webassign... i asked the professor and this is what he said:

First, draw a diagram showing the forces (including gravity) acting on the object. Next, pick a point of rotation. (Of course, you always pick a point that eliminates one or more of the unknowns.) And then, you apply the torque equation.

But thats exactly what i did... isnt it?

6. Nov 9, 2008

### Staff: Mentor

Yes, that's exactly what you did.

7. Nov 10, 2008

### avenkat0

Doc Al... i contacted him again and i was told, "Its not just a product but a CROSS PRODUCT"...
but in a vertical door arent all the torques exerted by gravity perpendicular??
im confused

8. Nov 10, 2008

### asleight

No, they're not all perpendicular. With respect to the axis of rotation, there is an angle between the radius and the force applied.

9. Nov 10, 2008

### Staff: Mentor

It certainly is a cross-product, not just a scalar product, but what you did was fine. To find the torque due to gravity, you took the force (mg) and multiplied it by the perpendicular component of the distance to the axis (W/2). All perfectly correct.

Similarly for the horizontal force supplied by the hinge.

What you did was completely correct.

To express the point more mathematically (for the torque due to gravity):
$$\tau = \vec{R} \times \vec{F} = RF\sin\theta = F(R\sin\theta) = mg (W/2) = mgW/2$$

Last edited: Nov 10, 2008