Question

Force F = (2.0 N) i + (-7.0 N) k acts on a pebble with position vector r = (0.60 m) j + (-0.9 m) k, relative to the origin. PLEASE SHOW WORK!

(a) What is the resulting torque acting on the pebble about the origin?

[ ] N·m i + [ ] N·m j + [ ] N·m k

(b) What is the resulting torque acting on the pebble about a point with coordinates (2.0 m, -8.0 m, 6.0 m)?

[ ] N·m i + [ ] N·m j + [ ] N·m k

Answer 1

here,

the force applied , F = ( 2 N) i + ( - 7 N) K

r = ( 0.6 m ) j + ( - 0.9 K)

a)

the resulting torque acting on the pebble about the origin , T = r X F

T = ( ( 0.6 m ) j + ( - 0.9 K)) X ( ( 2 N) i + ( - 7 N) K)

T = ( - 0.6 * 2 k - 4.2 i - 0.9 * 2 j)

T = ( - 4.2 i - 1.8 j - 1.2 k) N.m

b)

the position vector anout ( 2 m , - 8 m , 6 m) , r = ( (0 - 2 ) m i + ( 0.6 - (-8 m))j + ( - 0.9 - 6 m) K)

r = ( - 2 m i + 7.4 m j - 6.9 m k)

the resulting torque acting on the pebble about the origin , T = r X F

T = ( - 2 m i + 7.4 m j - 6.9 m k) X ( ( 2 N) i + ( - 7 N) K)

T = ( - 14 j - 14.8 k - 51.8 i - 13.8 j)

T = ( - 51.8 i - 27.8 j - 14.8 k) N.m