Calculate Torque: Vector Products Homework

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So for part (a), the resulting torque would be 32.19 Nm in the negative y direction. For part (b), we can use the formula torque = r x F, where r' = r - d. So for the point (5.0 m, 0, -1.7 m), the position vector would be (-1.3 m)j - (1.7 m)k. Therefore, the resulting torque would be -5.67 Nm in the negative y direction. In summary, the resulting torque acting on the pebble about the origin is 32.19 Nm in the negative y direction, and about the point (5.0 m, 0, -1.
  • #1
shell4987
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Homework Statement


Force = (8.7 N) - (4.2 N) acts on a pebble with position vector = (3.7 m) - (6.5 m), relative to the origin. What is the resulting torque acting on the pebble about (a) the origin and (b) a point with coordinates (5.0 m, 0, -1.7 m)?


Homework Equations


The cross product torque=rxf
r'=r-d


The Attempt at a Solution


I got part (a) correct, however I cannot get part (b) correct, I've done it about 5 times and it is completely wrong, my answers are: 0i + 6.21j + 0k. Can anyone tell me what I'm doing wrong?
 
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  • #2
How did one do the first part?

I'm a bit confused as to the position vector (3.7 m) - (6.5 m) and the pebble location. Is the pebble at the origin and the position vector is the moment arm of the force?
 
  • #3
Force is Force = (8.7 N)i - (4.2 N)k and position vector = (3.7 m)j - (6.5 m)k, which is relative to the origin
 

1. How do I calculate torque using vector products?

To calculate torque using vector products, you must first find the cross product of the force vector and the position vector. The magnitude of this cross product will give you the torque, and the direction of the torque will be perpendicular to both the force and position vectors, following the right-hand rule.

2. What is the formula for calculating torque using vector products?

The formula for calculating torque using vector products is T = r x F, where T is the torque, r is the position vector, and F is the force vector.

3. Can torque be negative when using vector products?

Yes, torque can be negative when using vector products. This occurs when the direction of the torque is opposite to the direction of the angular displacement.

4. How does the angle between the force and position vectors affect the torque calculation?

The angle between the force and position vectors affects the torque calculation by changing the magnitude of the cross product. The greater the angle between the vectors, the smaller the magnitude of the cross product and therefore, the smaller the torque.

5. What are some real-life applications of torque and vector products?

Torque and vector products have many real-life applications, such as in engineering and physics. They are used in designing and analyzing machines, calculating the forces and torques on structures, and understanding the motion of objects in rotational systems. They are also essential in fields such as robotics, biomechanics, and fluid mechanics.

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