The mobile in Fig. 74 is in equilibrium. Object B has mass of 0.748 kg . Determine the masses of

step 1 We have the bottom bar here. We know that each bar is in static equilibrium. So in order to find

The mobile in Fig. 74 is in equilibrium. Object B has mass...

The mobile in Fig. 74 is in equilibrium. Object $B$ has mass of
0.748 $\mathrm{kg}$ . Determine the masses of objects $\mathrm{A}, \mathrm{C},$ and $\mathrm{D}$ .(Neglect the weights of the crossbars.)

Key Concepts

Static Equilibrium

In mechanics, a system is in static equilibrium when it is at rest, meaning that the net force and the net torque acting on it are both zero. This concept is fundamental in statics and ensures that an object or system does not have any unbalanced forces that would cause translational or rotational motion.

Torque (Moment) Principle

Torque, or moment, is the rotational equivalent of force, defined as the product of the force and the lever arm (the perpendicular distance from the pivot point to the line of action of the force). For a system to be in rotational equilibrium, the sum of the clockwise torques must equal the sum of the counterclockwise torques.

Lever Arms and the Lever Principle

The lever arm is the distance from the pivot or fulcrum to the point where a force is applied. The lever principle, a key concept in mechanics, states that when different forces act on a rigid body at various distances from a pivot, equilibrium is achieved when the moments (i.e., force multiplied by its respective lever arm) balance out. This concept is crucial in analyzing systems like mobiles where the distribution of mass and distances affect balance.

Transcript

0:00 We have the bottom bar here.

00:01 We know that each bar is in static equilibrium.

00:04 So in order to find force subcd, we can apply the sum of torque.

00:12 This will equal zero, and this will equal m sub d, g, x, sub d, minus m sub c, g, x, c.

00:23 And so m sub c would be equalling m sub d times x sub d over x.

00:31 Sub c this is equaling m sub d multiplied by 17 .50 centimeters divided by 5 .00 centimeters this is giving us 3 .50 m sub d and so we can apply the sum of forces in the y direction this system has translational equilibrium in the y direction so this is going to equal zero and we can say that this is equaling force sub cd minus m sub c times g minus m sub d times g and so we find that force sub cd is equaling 4 .5 .0 m sub d times g and we can keep it we can keep just take uh keep in mind this relationship we then have the middle bar here again we're going to apply static equilibrium sum of torques is equaling zero this will equal force sub cd x sub cd minus m sub b g x sub b this is rather we find that force sub cd is then equaling m sub b g times x sub b divided by x sub cd and we can say that here 4 .50 m sub d g equaling m sub b g x sub b x sub b divided by x sub cd and so we can say that then m sub d is equalling m sub b x sub b divided by 4 .50 times x sub cd and we can solve so this would be 0 .748 kilograms multiplied by 5 .00 centimeters divided by 4 .50 multiplied by 15 .00 centimeters.

02:58 And so we find that mass sub d, this is equaling 0 .0554 kilograms.

03:10 We can then say that m sub c is equaling 3 .50 times m sub d.

03:17 This is equaling 3 .50 times 0 .0554.

03:26 This is equaling 0 .194 kilograms.

03:33 So we find mass sub d here, mass sub c here...

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