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
Answer:
d = 2021.6 km
Explanation:
This distance problem can be solved using vector analysis; it's best to find each plane's position components before applying the Pythagorean theorem to calculate the separation between them.
For Airplane 1:
Height y₁ = 800m
Angle θ = 25°
cos 25 = x / r
sin 25 = z / r
x₁ = r cos 20
z₁ = r sin 25
x₁ = 18 103 cos 25 = 16,314 103 m = 16314 m
z₁ = 18 103 sin 25 = 7,607 103 m = 7607 m
For Plane 2:
Height y₂ = 1100 m
Angle θ = 20°
x₂ = 20 103 cos 25 = 18.126 103 m = 18126 m
z₂ = 20 103 sin 25 = 8.452 103 m = 8452 m
To determine the distance between the planes using the Pythagorean theorem:
d² = (x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²2
Now, we perform the calculations:
d² = (18126-16314)² + (1100-800)² + (8452-7607)²
d² = 3,283 106 + 9 104 + 7,140 105
d² = (328.3 + 9 + 71.40) 10⁴
d = √(408.7 10⁴)
d = 20,216 10² m
d = 2021.6 km
The trailer that is loaded the most. The total weight does not matter; it is about how the load is distributed. For example, our 12,000 lb snow cat trailer has weight distribution that results in less than 100 lbs of tongue weight. Heavy tongue weight can create issues, as it can shift the weight off the front wheels of the towing vehicle, causing instability.
