magnitude of vectors (torque)

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rachelmaddie

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Hi. I need my work checked please.
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Torque is defined as T = r + F where r is the position vector of the point where the force is applied with respect to the point of rotation and F is the force vector.

Tamara’s forearm is 0.366 meters long so the force is being applied at a distance of 0.366 m from the point of rotation (her elbow). Her elbow is bent at an angle of 15° below the horizontal.

Another way to write it is the product of the radius and force magnitude * sine of the angle between vectors.
T = rF sin theta
where r = 0.366 meters and F = 155 Newtons. F is in the +y direction and r is below the +x axis, so the angle between vectors is 90° - 15° = 75°.
T = (0.366 m) (155 N) (sin 75°)
T = 54.8 N•m

54.8 N•m in the direction of the negative y-axis
 
rachelmaddie said:
Hi. I need my work checked please.
View attachment 20990
Torque is defined as T = r + F where r is the position vector of the point where the force is applied with respect to the point of rotation and F is the force vector.

Tamara’s forearm is 0.366 meters long so the force is being applied at a distance of 0.366 m from the point of rotation (her elbow). Her elbow is bent at an angle of 15° below the horizontal.

Another way to write it is the product of the radius and force magnitude * sine of the angle between vectors.
T = rF sin theta
where r = 0.366 meters and F = 155 Newtons. F is in the +y direction and r is below the +x axis, so the angle between vectors is 90° - 15° = 75°.
T = (0.366 m) (155 N) (sin 75°)
T = 54.8 N•m

54.8 N•m in the direction of the negative y-axis
Click to expand...
You say:

Torque is defined as

T = r + F ............................. that is incorrect.​

It should be:

T = r X F​

Where are your x and y axes? For moment problems that is very important consideration.

Were you provided with any picture/drawing of this problem?

The problem statement (without a drawing) is very ambiguous.

You say:

54.8 N•m in the direction of the negative y-axis​

This is incorrect. If the arm and the force lie in the x-y plane, the torque will be along the z-axis.
 
Subhotosh Khan said:
You say:

Torque is defined as

T = r + F ............................. that is incorrect.​

It should be:

T = r X F​

Where are your x and y axes? For moment problems that is very important consideration.

Were you provided with any picture/drawing of this problem?

The problem statement (without a drawing) is very ambiguous.

You say:

54.8 N•m in the direction of the negative y-axis​

This is incorrect. If the arm and the force lie in the x-y plane, the torque will be along the z-axis.
Click to expand...
No, there is no image. Did I do the steps incorrectly?
 
Subhotosh Khan said:
No.

Can you please post an image of a "torque" example-problem with solution, from which you learned to solve such problems?
Click to expand...
Actually the addition was just a mistake that I made on my part. I’m working on the problem again but i had to stop here at the Force vector before I proceed with the rest because I’m not sure if I’m doing it correctly.
Torque is defined as T = r x F where r is the position vector of the point where the force is applied with respect to the point of rotation and F is the force vector.

Tamara’s forearm is 0.366 meters long so the force is being applied at a distance of 0.366 m from the point of rotation (her elbow). Since her elbow is bent at an angle of 15° below the horizontal, then the position vector is r = (0.366 cos(-15°), 0, 0.366 sin(-15°)) = (0.353, 0, -0.094). Note that the angle is -15° since the angle is below the horizontal.

The force being applied is only in the vertical direction so F = (0, 0,155).
Therefore:
T = r x F
= (0.353, 0, -0.094) x (0, 0,155)
 
Can you please post an image of a "torque" example-problem with solution, from which you learned to solve such problems?
 
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