Which of these nebulae is the odd one out?
2 answers:
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<h2>Question
</h2>
A particle, mass 0.25 kg is at a position (<em>-7i + 7j + 5k</em>) m, has a velocity (<em>6i - j + 4k</em>) m/s, and is subject to a force (<em>-5i + 0j - k</em>) N. What is the magnitude of the torque on the particle about the origin?
<h2>Answer:</h2>
47.94Nm
<h2>Explanation:</h2>The torque (τ) on a particle subject to a force (represented as force vector F) at a position (represented as position vector r) about the origin is given by the cross product of the position vector r for the point of application of a force and the force F. i.e
τ = r x F
Given:
r = (-7i + 7j + 5k) m
F = (-5i + 0j - k) N
| i j k |
r x F = | -7 7 5 |
| -5 0 -1 |
r x F = i(-7 - 0) - j(7+25) + k(0+35)
r x F = i(-7) - j(32) + k(35)
r x F = -7i - 32j + 35k
Therefore the torque τ = -7i - 32j + 35k
The magnitude of the torque is therefore;
|τ| =
|τ| =
|τ| =
|τ| = 47.94Nm
The magnitude of the torque on the particle about the origin is 47.94Nm
Answer:
Efficiency: 0.4 (40%)
Explanation:
The efficiency of a simple machine is given by the ratio
where
is the input work of the machine
is the output work of the machine
For the machine in this problem, we have:
is the output work
is the input work
Therefore, the efficiency of the machine is
Which can be also written as percentage: