Calculating Net Force on a Wheel: Magnitude and Direction | 0.350 m Radius

AI Thread Summary
Three forces are acting on a wheel with a radius of 0.350 m, including one perpendicular to the rim, one tangent, and another at a 40-degree angle. The user calculated the net force (Fnet) to be approximately 14.4 N at an angle of -3.44° but is uncertain about the relevance of net force to net torque due to the forces not being applied at the same point. It is clarified that net force and net torque are distinct concepts and should not be directly related in this context. The exercise aims to reinforce understanding of vector addition and the differences between force and torque. This distinction is crucial for solving related physics problems effectively.
omal3rab
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Homework Statement
Three forces are applied to a wheel of radius 0.350 m, as shown in the figure. One force is perpendicular to the rim, one is tangent to it, and the other one makes a 40.0 degree angle with the radius, and a 10 degree angle with the horizontal.


a) What is the magnitude of the net force on the wheel? [3 marks]
Relevant Equations
Fnet = sqrt(Fnetx^2 + Fnety^2)
tan(theta)= Fnety/Fnetx
Screenshot (367).png


Three forces are applied to a wheel of radius 0.350 m, as shown in the figure. One force is perpendicular to the rim, one is tangent to it, and the other one makes a 40.0 degree angle with the radius, and a 10 degree angle with the horizontal.

a) What is the magnitude of the net force on the wheel? [3 marks]


I am having trouble with Part a) of this problem, I got Parts b) and c) correct, but theres no answer available for a). I don't know whether I should relate Fnet to 𝜏net. I feel like I shouldn't, since the forces are not all being applied to the same point. I got an answer of Fnet = 14.4 N [-3.44°], is this correct? I made my coordinate system positive going up and to the right, made Fnetx and Fnety statements, then related them by Pythagorean Theorem.

Fnetx: 14.6cos(10) = 14.3782 N
Fnety: 8.5 + 14.6sin(10) - 11.9 = -0.86 N
theta = arctan(0.86/14.3782) = 3.44° (below horizontal, hence the negative sign above)
Fnet: sqrt((14.3782)^2 +(-0.86)^2)) = 14.404 N
 
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omal3rab said:
View attachment 335410I am having trouble with Part a) of this problem, I got Parts b) and c) correct, but theres no answer available for a). I don't know whether I should relate Fnet to 𝜏net. I feel like I shouldn't, since the forces are not all being applied to the same point. I got an answer of Fnet = 14.4 N [-3.44°], is this correct? I made my coordinate system positive going up and to the right, made Fnetx and Fnety statements, then related them by Pythagorean Theorem.

Fnetx: 14.6cos(10) = 14.3782 N
Fnety: 8.5 + 14.6sin(10) - 11.9 = -0.86 N
theta = arctan(0.86/14.3782) = 3.44° (below horizontal, hence the negative sign above)
Fnet: sqrt((14.3782)^2 +(-0.86)^2)) = 14.404 N
Looks ok to me.
 
erobz said:
Looks ok to me.
Thank you! Does this mean I am correct in my assumption that I can't relate Fnet to Torque net since the forces are not all being applied to the same point? I'm still confused on what's the point of this question, since it doesn't help me solve the next part. I could be overthinking this, but it just seems odd.
 
omal3rab said:
Thank you! Does this mean I am correct in my assumption that I can't relate Fnet to Torque net since the forces are not all being applied to the same point? I'm still confused on what's the point of this question, since it doesn't help me solve the next part. I could be overthinking this, but it just seems odd.
It's an exercise in vector addition, I wouldn't over think it. The net torque is a different quantity from the net force.
 
omal3rab said:
Does this mean I am correct in my assumption that I can't relate Fnet to Torque net since the forces are not all being applied to the same point?
Yes.
omal3rab said:
what's the point of this question, since it doesn't help me solve the next part
The point is either to check you understand the difference or perhaps to drive home that they are different.
 
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