Calculating torque about a point with given forces

In summary, the conversation discusses solving for the net torque on point A using the given forces and their angles. One participant found the same answer as the other but with a simpler solution, and they also mentioned an error in the given answer for the problem. The conversation ends with a new member being welcomed.
  • #1
Nova_Chr0n0
16
3
Homework Statement
What is the net torque around point A?
Relevant Equations
τ = rF
wew1.JPG

I've inserted a photo of the figure, hope everyone can see it.

SOLUTION:
1. I first solved for the angle of 100 N and 50 N since I need the force that is perpendicular to point A.
>> Angle of 100 N
theta = arctan(3/4)
theta = 36.870 degree
>> Angle of 50 N
theta = arctan(12/5)
theta = 67.380 degree
2. Solving for the net torque on point A where counter-clockwise is + and clockwise is -
τ = rF
τ_A = -1[100sin(36.870)] - 1.75(70) - 2[50sin(67.380)]
τ_A = -274.808 Nm

My final answer for the torque at point A is -274.808 Nm, but when I check the answer in the textbook, it is -295 Nm. I am confused about what part I did wrong. Also, I'm new to the forum, so if my format is not understandable, kindly inform me about it. Thanks!
 
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  • #2
Finding the angles was rather unnecessary since you are given the right triangle ratios. You could just write 100N x 1m x (3/5) etc.
But I get the same answer as you do.
 
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  • #3
Well, I've got 274.8 as well, though my solution is somewhat less convolute than yours.

Is there anything else to the question ?
 
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  • #4
  • #5
haruspex said:
Finding the angles was rather unnecessary since you are given the right triangle ratios. You could just write 100N x 1m x (3/5) etc.
But I get the same answer as you do.
I guess there was just an error in the given answer for the file that I've encountered. Also, thanks for letting me know a solution with less work when involving triangle ratios. Really appreciate it!
 
  • #6
Nova_Chr0n0 said:
I guess there was just an error in the given answer for the file that I've encountered. Also, thanks for letting me know a solution with less work when involving triangle ratios. Really appreciate it!
Welcome, @Nova_Chr0n0 !

That dimension of 1 m to the right of the figure suggests that either a force that is applied at the right end, or the weight of the 3-meter bar, is missing.
 
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FAQ: Calculating torque about a point with given forces

What is torque and how is it calculated?

Torque is a measure of the rotational force applied to an object around a pivot point. It is calculated as the product of the force applied and the perpendicular distance from the pivot point to the line of action of the force. Mathematically, torque (τ) is given by the equation τ = r × F, where r is the position vector (distance from the pivot point) and F is the force vector.

How do you determine the direction of the torque?

The direction of the torque is determined using the right-hand rule. Point your right hand's fingers in the direction of the position vector (r) and curl them towards the force vector (F). Your thumb will point in the direction of the torque. If the thumb points out of the plane, the torque is positive (counterclockwise), and if it points into the plane, the torque is negative (clockwise).

What is the significance of the pivot point in torque calculations?

The pivot point, or axis of rotation, is crucial in torque calculations because torque is always calculated relative to this point. The position vector (r) is measured from the pivot point to the point where the force is applied. Changing the pivot point can change the magnitude and direction of the torque, even if the force remains the same.

How do you calculate torque when multiple forces are acting on an object?

When multiple forces are acting on an object, the net torque is the vector sum of the individual torques produced by each force. Calculate the torque produced by each force using τ = r × F, and then sum these torques to find the total or net torque. Be sure to consider the direction (sign) of each torque when summing them up.

Can torque be zero even if forces are acting on an object?

Yes, torque can be zero even if forces are acting on an object. This can happen if the forces are balanced and produce equal and opposite torques that cancel each other out, or if the forces are applied in such a way that their lines of action pass through the pivot point, resulting in no rotational effect. For instance, if two equal forces are applied in opposite directions at equal distances from the pivot point, their torques will cancel out, resulting in a net torque of zero.

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