Complete Question
A 30 cm cm wrench is employed to loosen a bolt, with force applied 0.30m from the bolt. It requires 60 N to loosen the bolt when force is applied perpendicular to the wrench. How much force would be necessary if the force were applied at a 30-degree angle from perpendicular?
Response:
The strength needed is 
Clarification:
According to the problem, we know that
The length of the wrench is 
The distance from the bolt is 
The force necessary to loosen the bolt is 
The angle of application is 
Generally, the torque required for loosening the bolt is defined as
Now for the bolt to loosen at 
the torque at 90° must equal that at
Thus, the torque at is represented mathematically as
substituting values gives us
It is stated that, in a typical pulsed-field machine, the magnetic field rises from 0 T to 2.5 T within 200 μs. The change in the magnetic field and time interval are relevant here. The diameter is 2.3 cm, translating to a radius of 0.0115 m. As the magnetic field changes, an induced emf occurs within the ring, determined by: E = 5.19 volts. Thus, the induced emf in the ring equates to 5.19 volts, which is the sought solution.
Response:
0.9 cm
Clarification:
The following illustrates the calculation of the combined rod's length increase:
As established
Length increase = expansion of aluminum rod + expansion of steel rod
= 0.9 cm
We simply summed the expansions of both the aluminum and steel rods to determine the overall increase in the joined rod's length, which must be factored in
