Calculate the z component of the torque relative to position

In summary: Cross_productIn summary, the problem involves calculating the z component of the torque relative to position A, given seven forces with a magnitude of 32 N, a distance of 10 m, a height of 16 m, and a distance of 15 m. The solution involves using the equation T = r X F and taking into account the direction of the torque using the right hand rule. The z component of the torque for each force can be calculated by taking the cross product of the distance and the force, and then multiplying it by the direction of the torque (either clockwise or counterclockwise). The net torque can then be determined by summing up all of the individual torques.
  • #1
magma_saber
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Homework Statement


http://img3.imageshack.us/img3/5681/32832.jpg

All seven forces have a magnitude |F| = 32 N. w = 10 m, h = 16 m, and d = 15 m. Calculate the z component of the torque relative to position A.

Homework Equations


T = r*F


The Attempt at a Solution


Not sure how to start this.
F1 = F*h*w = 32*16*10?
F2 = F*h = 32*16?
 
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  • #2


T = r X F

So you want to figure the force acting at a perpendicular to the point at interest.

In this case your r X F1 will equal |F1|*h, where h is the distance at which it is acting ⊥ to a line through A.
 
  • #3


LowlyPion said:
T = r X F

So you want to figure the force acting at a perpendicular to the point at interest.

In this case your r X F1 will equal |F1|*h, where h is the distance at which it is acting ⊥ to a line through A.

i tried that, its wrong. it says the z component. would that make a difference?
 
  • #4


magma_saber said:
i tried that, its wrong. it says the z component. would that make a difference?

The resultant of r X F is a z component by the right hand rule for taking a cross product.

Of course you still need to sum up all the other torques from the other forces.
 
  • #5


it asks just for the torque for each force that is applied, i.e. F1, F2, F3, ect. After that, it asks for the net torque. for F1 i tried F*h and it was wrong. Would it be F*h*w, since the tail starts at w?
 
  • #6


magma_saber said:
it asks just for the torque for each force that is applied, i.e. F1, F2, F3, ect. After that, it asks for the net torque. for F1 i tried F*h and it was wrong. Would it be F*h*w, since the tail starts at w?

Sorry I thought you were supposed to be determining the sum.

The |T| is F1*h. But because it is the cross product of y X x, that yields a clockwise torque that is -z

So for F1 you have the z component is -|F1*h|z

Counterclockwise torques are positive. Clockwise are negative.
http://en.wikipedia.org/wiki/Right-hand_rule
 

FAQ: Calculate the z component of the torque relative to position

1. What is torque and how is it calculated?

Torque is a measure of the force that causes an object to rotate. It is calculated by multiplying the force applied to the object by the perpendicular distance from the point of rotation to the line of action of the force.

2. What is the z component of torque?

The z component of torque is the component of torque that is perpendicular to both the force and the distance vector. It is also known as the cross product of the force and distance vectors.

3. How do you calculate the z component of torque?

The z component of torque can be calculated by taking the cross product of the force vector and the distance vector. This is done by multiplying the magnitude of the force by the magnitude of the distance and then multiplying it by the sine of the angle between the two vectors.

4. Why is it important to calculate the z component of torque?

The z component of torque is important because it determines the direction of rotation for an object. If the z component is positive, the object will rotate in a counterclockwise direction, and if it is negative, the rotation will be clockwise.

5. How is the z component of torque used in real-world applications?

The z component of torque is used in many real-world applications, such as engineering, physics, and mechanics. It is essential for understanding the stability and balance of structures, calculating the movement of objects, and designing machines and mechanisms.

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