Explanation:
The x component of the resultant force is the sum of the x components of the individual forces.
Fₓ = 65.0 cos 30° − 20.0 sin 20° − 30.0
Fₓ = 19.5
The y component of the resultant force is the sum of the y components of the individual forces.
Fᵧ = 65.0 sin 30° − 20.0 cos 20°
Fᵧ = 13.7
The magnitude is found with Pythagorean theorem:
F² = Fₓ² + Fᵧ²
F² = (19.5)² + (13.7)²
F = 23.8
Answer:
Since the wire is not splitting at any point in the circuit,
the resistors are in series
Hence, Equivalent resistance = 10 + 20 + 30
Equivalent Resistance = 60 Ω
Sure.
Can I use your answer to part-'a' ?
If the angular acceleration is actually 32 rev/min², than
after 1.2 min, it has reached the speed of
(32 rev/min²) x (1.2 min) = 38.4 rev/min .
Check:
If the initial speed is zero and the final speed is 38.4 rpm,
then the average speed during the acceleration period is
(1/2) (0 + 38.4) = 19.2 rpm average
At an average speed of 19.2 rpm for 1.2 min,
it covers
(19.2 rev/min) x (1.2 min) = 23.04 revs .
That's pretty close to the "23" in the question, so I think that
everything here is in order.
Assuming that the vectors are acting along the same axis, we
could just simply add or subtract the vectors. Since the F1 is greater than F2,
there would be motion, there would be acceleration, and that the direction of
motion is along the F1.
The angular acceleration of the blade when it's switched off is (-6800 rev/min) divided by (2.8 sec) = -2,428.6 rev/(min-sec) = -40.5 rev/sec^2 .
