Two forces equal in magnitude and opposite in direction,...

Two forces equal in magnitude and opposite in direction, acting on an object at two different points, form what is called a couple. Two antiparallel forces with equal magnitudes $F_{1}=F_{2}=8.00 \mathrm{~N}$ are applied to a rod as shown in Fig. $\mathbf{E 1 1 . 2 3}$ (a) What should the distance $l$ between the forces be if they are to provide a net torque of $6.40 \mathrm{~N} \cdot \mathrm{m}$ about the left end of the rod? (b) Is the sense of this torque clockwise or counterclockwise? (c) Repeat parts (a) and (b) for a pivot at the point on the rod where $\overrightarrow{\boldsymbol{F}}_{2}$ is applied.

Two forces equal in magnitude and opposite in direction, acting on an object at two different points, form what is called a couple. Two antiparallel forces with equal magnitudes $F_{1}=F_{2}=8.00 \mathrm{~N}$ are applied to a rod as shown in Fig. $\mathbf{E 1 1 . 2 3}$
(a) What should the distance $l$ between the forces be if they are to provide a net torque of $6.40 \mathrm{~N} \cdot \mathrm{m}$ about the left end of the rod? (b) Is the sense of this torque clockwise or counterclockwise?
(c) Repeat parts
(a) and (b) for a pivot at the point on the rod where $\overrightarrow{\boldsymbol{F}}_{2}$ is applied.

Key Concepts

Couple

A couple is a pair of equal and opposite forces whose lines of action are parallel but not collinear. This configuration produces a net torque (moment) on the object without resulting in any net force, leading to pure rotational motion about a pivot.

Torque

Torque is the measure of the rotational effect of a force acting at a distance from a pivot. It is calculated as the product of the force and the lever arm (perpendicular distance from the pivot to the force's line of action) and is fundamental in analyzing rotational equilibrium.

Lever Arm

The lever arm, or moment arm, is the perpendicular distance from the axis of rotation (pivot) to the line along which the force acts. It magnifies the effect of the force in producing rotational motion.

Pivot Point

The pivot point is the fixed point or axis about which an object rotates. In torque calculations, although the net torque produced by a couple is independent of the pivot, choosing an appropriate pivot can simplify problem analysis.

Sign Convention

The sign convention in torque analysis determines whether a torque is considered positive (typically counterclockwise) or negative (typically clockwise). This systematic approach ensures consistency in identifying the direction of rotational effects.

Transcript

00:01 Hi, here in this given problem this is an object in the form of a rod hinged at point o, two forces which are anti -parallel to each other, f1 and f2, acting on the object having a gap l between them and the distance of line of action of the first force from hinged point that is 3 .00 meter.

00:31 Magnitude of both of these forces.

00:34 F1 that is equal to f2 which is 8 .00 newton.

00:40 In the first part of the problem net torque acting on this beam that will be given by clockwise torque created by f2 means f2 multiplied by perpendicular distance from hinge which is 3 .00 plus l and minus counterclockwise torque created by f1 so this is f1 multiplied by 3 .00.

01:17 And this torque is given as for f2 and f1 this is 8.

01:21 And 8 can be taken out as a common leaving behind 3 plus l minus 3.

01:27 And this torque is given as 6 .40 newton into meter canceling this 3.

01:34 L will be given by 6 .40 divided by 8.

01:39 Means this is 0 .80 meter.

01:45 Answer for the first part of the problem.

01:49 The gap between two anti -parallel forces.

01:53 Then in the second part, this net force, direction of this net force that is clockwise because f2 is greater.

02:01 So torque created by it will be, sorry, torque created by f2 is greater than that created by f1.

02:10 So net torque is in the direction of torque created by f2 and this is clockwise...