Four masses are positioned at the corners of a rectangle, asindicated in the fig

Question

Four masses are positioned at the corners of a rectangle, asindicated in the figure . 1.) Find the magnitude of the net forceacting on the 2.0-kg mass. F = ? N 2.) Find the direction of the net forceacting on the 2.0-kg mass. ______ degrees below horizontal and to theleft. 3.) How do your answers to parts A and Bchange (if at all) if all sides of the rectangle are doubled inlength? 1.) Find the magnitude of the net forceacting on the 2.0-kg mass. F = ? N 2.) Find the direction of the net forceacting on the 2.0-kg mass. ______ degrees below horizontal and to theleft. 3.) How do your answers to parts A and Bchange (if at all) if all sides of the rectangle are doubled inlength? 2.) Find the direction of the net forceacting on the 2.0-kg mass. ______ degrees below horizontal and to theleft. 3.) How do your answers to parts A and Bchange (if at all) if all sides of the rectangle are doubled inlength? 3.) How do your answers to parts A and Bchange (if at all) if all sides of the rectangle are doubled inlength?

Explanation / Answer

1.)Let the four masses be m1 = 1.0 kg,m2= 2.0 kg,m3 = 3.0 kg and m4 = 4.0 kg
The force acting between the masses m1 and m2is F1 =(Gm1m2/r12) where G = 6.67 * 10-11Nm2/kg2 and r1 = 0.20 m The force acting between the masses m2 andm3 is F2 =(Gm2m3/r22) where r2 = 0.10 m The force acting between the masses m2 andm4 is F3 =(Gm2m4/r32) where r3 = 0.5 m The magnitude of the net force acting on the 2.0-kg massis F = (Fx2 +Fy2)1/2 where Fx = F1x + F2x +F3x = F1 * cos1 +F2 * cos2 + F3 *cos3 and Fy = F1y + F2y +F3y = F1 * sin1 +F2 * sin2 + F3 *sin3 where 1 = 2 = 0oand 3 = 45o 2.)The direction of the net force acting on the 2.0-kg massis tan = (Fy/Fx) or = tan-1(Fy/Fx)degrees below horizontal and to the left 3.)When all sides of the rectangle are doubled in length,thenthe forces F1,F2 and F3 become(1/4) of the original value and hence the net force also becomes(1/4).The direction of the net force remains unchanged. The force acting between the masses m2 andm3 is F2 =(Gm2m3/r22) where r2 = 0.10 m The force acting between the masses m2 andm4 is F3 =(Gm2m4/r32) where r3 = 0.5 m The magnitude of the net force acting on the 2.0-kg massis F = (Fx2 +Fy2)1/2 where Fx = F1x + F2x +F3x = F1 * cos1 +F2 * cos2 + F3 *cos3 and Fy = F1y + F2y +F3y = F1 * sin1 +F2 * sin2 + F3 *sin3 where 1 = 2 = 0oand 3 = 45o 2.)The direction of the net force acting on the 2.0-kg massis tan = (Fy/Fx) or = tan-1(Fy/Fx)degrees below horizontal and to the left 3.)When all sides of the rectangle are doubled in length,thenthe forces F1,F2 and F3 become(1/4) of the original value and hence the net force also becomes(1/4).The direction of the net force remains unchanged. The force acting between the masses m2 andm4 is F3 =(Gm2m4/r32) where r3 = 0.5 m The magnitude of the net force acting on the 2.0-kg massis F = (Fx2 +Fy2)1/2 where Fx = F1x + F2x +F3x = F1 * cos1 +F2 * cos2 + F3 *cos3 and Fy = F1y + F2y +F3y = F1 * sin1 +F2 * sin2 + F3 *sin3 where 1 = 2 = 0oand 3 = 45o 2.)The direction of the net force acting on the 2.0-kg massis tan = (Fy/Fx) or = tan-1(Fy/Fx)degrees below horizontal and to the left 3.)When all sides of the rectangle are doubled in length,thenthe forces F1,F2 and F3 become(1/4) of the original value and hence the net force also becomes(1/4).The direction of the net force remains unchanged.

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.