2. Consider a system that consists of three particles: a mass of 10kg lies at th

Question

2. Consider a system that consists of three particles: a mass of 10kg lies at the point (1m, 0), a mass of 2 kg lies at the point(2m,1m), and a mass of 5 kg lies at the point (0,1m), as shown inthe figure

(m=meter). On the 10 kg particle, there is a force of 10 N in thepositive x direction. On the 2 kg particle, there is a force of 5 Ninclined 45 o above horizontal. Finally, on the 5 kg particle,there is a force of 2 N in the negative y direction. Find (a) thecenter of mass of the three-particle system, and (b) the resultantacceleration (magnitude and direction) of the system.

Explanation / Answer

(a) the center of mass of the three-particlesystem x<C>=(10*1+2*2 +5*0)/(5+10+2)=0.824 m y<C>=(10*0 +2*1+5*1)/(5+10+2)=0.412 m =>center:(0.824,0.412) (b)the resultant acceleration of the system in x-axis : ax=(10+5*cos45)/17=0.796 m/s2 in y-axis : ay=(-2 +5*sin45)/17=0.09 m/s2 => magnitude a=(ax2+ay2)=0.801m/s2 direction tan=ay/ax=0.113 => =6.450 direction tan=ay/ax=0.113 => =6.450

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