A wheel of radius R with an axle of radius R/ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The net torque $	au_{	ext{net}}$ is the sum of the torques produced by each force about the central axis.$1$. Torque due to force $F$ at the out

Vedclass · Accepted Answer

$3.2$

Vedclass · Answer

(B) The net torque $	au_{	ext{net}}$ is the sum of the torques produced by each force about the central axis.$1$. Torque due to force $F$ at the outer rim (at $45^{\circ}$): The tangential component of this force is $F \cos(45^{\circ})$. The torque is $	au_1 = R \cdot F \cos(45^{\circ}) = R \cdot F \cdot \frac{1}{\sqrt{2}} \approx 0.707 RF$.$2$. Torque due to force $F$ at the inner axle: This force is applied tangentially at radius $R/2$. The torque is $	au_2 = \frac{R}{2} \cdot F = 0.5 RF$.$3$. Torque due to force $2F$ at the outer rim: This force is applied tangentially at radius $R$. The torque is $	au_3 = R \cdot 2F = 2 RF$.All these torques act in the same rotational sense (counter-clockwise). Therefore,the net torque is:$	au_{	ext{net}} = 	au_1 + 	au_2 + 	au_3 = 0.707 RF + 0.5 RF + 2 RF = 3.207 RF$.Rounding to the nearest value,the magnitude of the net torque is nearly $3.2 FR$.

Similar Questions

If $\vec{F}$ is the force acting on a particle having position vector $\vec{r}$ and $\vec{\tau}$ is the torque of this force about the origin,then

What is a couple? Give its illustrations.

The center of an equilateral triangle $ABC$ is $O$. Three forces $F_1$,$F_2$,and $F_3$ are applied along the sides $AB$,$BC$,and $AC$ respectively. If the total torque about $O$ is zero,what is the relationship between $F_1$,$F_2$,and $F_3$?

When a force of $6.0 \, N$ is exerted at $30^{\circ}$ to a wrench at a distance of $8 \, cm$ from the nut,it is just able to loosen the nut. What force $F$ would be sufficient to loosen it,if it acts perpendicularly to the wrench at $16 \, cm$ from the nut (in $, N$)?

$A$ couple produces:

Vedclass Test Series

Exam Paper Generator

Online Exam Module