Question

In unit-vector notation, what is the net torque about the origin on a flea located at coordinates (-2.0, 1.0 m, 1.0 m) when forces F1 = (1.0 N) k and F2 = (-2.0 N) j act on the flea?

Answer 1

The net torque about the origin of a flea located at coordinates (-2.0, 1.0 m, 1.0 m) is 3.0î m².

Step-by-step explanation:

The net torque about the origin of a flea located at coordinates (-2.0, 1.0 m, 1.0 m) can be found by multiplying each force by the corresponding position vector and then taking the sum of the torques. In this case, force F1 = (1.0 N) k and force F2 = (-2.0 N) j act on the flea. The position vector r = (-2.0î + 1.0ĵ + 1.0k) m. To find the torque due to each force, we use the formula τ = r × F. Calculating the torque due to F1 results in (1.0 N)(1.0k) = -1.0î m². Calculating the torque due to F2 results in (-2.0 N)(-2.0ĵ) = 4.0î m². Adding these torques together gives the net torque about the origin: (-1.0î m²) + (4.0î m²) = 3.0î m². So, the net torque about the origin of the flea located at coordinates (-2.0, 1.0 m, 1.0 m) is 3.0î m²

Answer 2

Torque,
`\tau=3i+2j+4k`

Step-by-step explanation:

Given that,

Position of the flea,
`r=(-2i+j+k)\ m`

Force acting on the flea,
`F=(-2j+k)\ N`

We need to find the net torque about the origin on a flea located at coordinates. Its formula is given by :

`\tau=r* F`

`\tau=(-2i+j+k) * (-2j+k)`

On solving the cross product of r and F, we get :

`\tau=3i+2j+4k`

So, the net torque about the origin on a flea is
`3i+2j+4k`. Hence, this is the required solution.