Answer:
i. 0.2 N ii. 30°
Explanation:
(i) Calculate the magnitude and direction of force on X, when a current of 4A is passed through it.
The magnetic force F = BILsinФ where B = magnetic field strength = 0.1 T, I = current = 4 A and L= length of conductor = 0.5 m. Since the conductor X of length 0.5m is held along the positive X-axis and situated in a uniform horizontal magnetic field of 0.1T which is pointing towards the positive Y-axis, both B and L are perpendicular to each other. So, Ф = 90°
So, F = BILsinФ
F = 0.1 T × 4 A ×0.5 m × sin90°
F = 0.1 T × 4 A ×0.5 m × 1
F = 0.2 N
(ii) Through what angle must X be turned in a vertical plane so that the force on X is halved
If F' = BILsinФ' where Ф'=the new angle, and BIL = F
F'/F = sinФ'
Since F'/F = 1/2
sinФ' = 1/2
Ф' = sin⁻¹(1/2) = 30°
Answer:
X Component is 183.85N
Explanation:
The x component of the force on the block due to the rope;
X = F cos @ where if is the force, @ is the angle mad with the block.
X = F cos @
X = 240 cos 40
Cos 40= 0.7660, so
X = 240 × 0.7660
X component= 183.85N// rounded to two decimal places.
Answer:
The acceleration of a point on the wheel is 11.43 m/s² acting radially inward.
Explanation:
The centripetal acceleration acts on a body when it is performing a circular motion.
Here, a point on the bicycle is performing circular motion as the rotation of the wheel produces a circular motion.
The centripetal acceleration of a point moving with a velocity 
and at a distance of 
from the axis of rotation is given as:
Here, 
∴ 
Therefore, the acceleration of a point on the wheel is 11.43 m/s² acting radially inward.
