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:
Explanation:
The measurement of pressure is indicated as 
where p denotes the pressure, 
signifies density, and h represents height
Given values include pressure 
, gravity's acceleration 
, and height =1.163 m
Answer:
Explanation:
at 23 degrees Celsius, the diameter measures 4.511 mm
GIVEN DATA:
diameter of hole = 4.500 mm
T_1 = 23.0 degrees Celsius
T_2 = - 78.0 degrees Celsius
the expansion coefficient of aluminum is 2.4*10^{-5} (degrees Celsius)^{-1}
the diameter at 23 degrees Celsius is stated as
= 4.511 mm
the diameter of the rivet after temperature change is given as
= 0.4511 cm
U = 1794.005 × 10⁶ J. Explanation: Information provided indicates that the capacitance of the original capacitor is C = 1.27 F, and the potential difference applied to it is V = 59.9 kV, or 59.9 × 10³ V. The potential energy (U) for the capacitor is determined by the formula: U = (1/2) × C × V². Substituting the respective values, we find U = (1/2) × 1.27 × (59.9 × 10³)², resulting in U = 1794.005 × 10⁶ J.
Objects in vertical motion are an illustration of non-uniform motion. At the peak of the circle, centripetal force is balanced by the object's weight. Therefore, the minimum speed required at this top point is given by v =
=
= 5.23 m/s. As the sphere descends from the top to the bottom of the circle, according to the law of conservation of energy, potential energy can be expressed as
, where h signifies the diameter of the circle (2r). Hence, the expression will be written as
where u is the velocity at the lowest point. Consequently, the modified equation is
= 
= 
= 11.71 m/s. The collision of the dart with the bullet is an inelastic one. According to the conservation of momentum: v = 
= 
= 
= 58.55 m/s. Thus, the dart's minimum initial speed for the combined system to complete a circular loop post-collision is 58.55 m/s.
