Two forces F1 and F2 are acting on a mass M=3kg. The force F1 = 5i + 4j + 7k, in N. The acceleration of the mass is given by a = 3i + 7j + 5k, in m/s2. Calculate the magnitude of F2?
Is the magnitude of a force vector in Newtons? How do I do this problem?
Is the magnitude of a force vector in Newtons? How do I do this problem?
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Let’s assume F2=ai+bj+ck
then according Newton’s law of motion F=ma
F1+F2=ma
(5i+4j+7k)+( ai+bj+ck)=3(3i+7j+5k)
(5+a)i+(4+b)j+(7+c)k=9i+21j+15k
thus a=4 b=17 c=8
F2=4i+17j+8k
the magnitude of F2=sqrt(4^2+17^2+8^2)
=3sqrt(41) N≒19.2N
then according Newton’s law of motion F=ma
F1+F2=ma
(5i+4j+7k)+( ai+bj+ck)=3(3i+7j+5k)
(5+a)i+(4+b)j+(7+c)k=9i+21j+15k
thus a=4 b=17 c=8
F2=4i+17j+8k
the magnitude of F2=sqrt(4^2+17^2+8^2)
=3sqrt(41) N≒19.2N