8. 416 points I Previous Answers SerPSE9 11.P.008 My Notes Ask Your Teach A part

Question

8. 416 points I Previous Answers SerPSE9 11.P.008 My Notes Ask Your Teach A particle is located at the vector position r (8.00 9.00j) m and a force exerted on it is given by F (7.00 6.00j) N. (a) What is the torque acting on the particle about the origin? (-13) k T E (b) Can there be another point about which the torque caused by this force on this particle will be in the opposite direction and half as large in magnitude? Yes No (c) Can there be more than one such point? Yes No (d) Can such a point lie on the y axis? Yes O No (e) Can more than one such point lie on the y axis? O Yes No (f) Determine the position vector of one such point. (Give a point on the y axis.) (3) j X m

Explanation / Answer

(a) r = 8 i + 9 j

F = 7 i + 6 j

Torque = r x F

= ( 8 i + 9 j ) x ( 7 i + 6 j )

= 56 (i x i) + 48 ( i x j ) + 63 ( j x i) + 54 x ( j x j)

= 0 + 48 k - 63 k + 0

= - 15 k

So, Torque = (-15) k N/m

(f) Le the position be r = y j

Torque = - 0.5 * ( - 15 k ) = 7.5 k N/m

r x F = 7.5 k

y j x (7 i + 6 j ) = 7.5 k

7 ( j x i ) + 6 y ( j x j ) = 7.5 k

- 7 j k = 7.5 k

j = - 7.5 / 7 = - 1.0714 m

r = - 1.0714 j m

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