Balance of vertical forces problem. Three balanced forces pull on a ring that is centered over a force table. Two forces F1 and F2 are due to weights hanging from pulleys. A frictionless pulley changes the direction of a force without altering its magnitude. The third force F3 is applied by a string that passes over a pulley and pulls on the force transducer.
EXAMPLE:
>From the balance of vertical forces, derive the expected value of theta2 in terms of m1, m2, and theta1.
[Answer: theta2=sin^(-1)[m1sin1/m2).]
Which equation is NOT used in the derivation?
A. F=ma
B. F=mg
C. Fg=Fsin(theta)
D. Fg=Fcos(theta)
The answer is D. Fg=Fcos(theta)
Well, let's eliminate some options here.
A. F=ma is a fundamental equation in physics, so it's definitely used in the derivation. We're dealing with forces, so this equation is necessary.
B. F=mg represents the force due to gravity acting on an object, so it's also essential in calculating the forces involved.
C. Fg=Fsin(theta) deals with the component of the gravitational force that acts parallel to an inclined plane. Since we're dealing with vertical forces here, we don't need this equation for the derivation.
That leaves us with one option:
D. Fg=Fcos(theta). This equation deals with the component of the gravitational force that acts perpendicular to an inclined plane. Again, since we're dealing with vertical forces, we don't need this equation for the derivation.
Therefore, the equation that is NOT used in the derivation is D. Fg=Fcos(theta). Keep that in mind when solving the problem, and you'll be good to go!
The equation that is NOT used in the derivation is D. Fg=Fcos(theta).
To determine which equation is not used in the derivation of the expected value of theta2, we need to understand the forces involved in the problem and how they affect the motion of the ring.
Let's analyze each equation provided:
A. F = ma: This equation represents Newton's second law, which states that the resultant force acting on an object is equal to the mass of the object multiplied by its acceleration. This equation is commonly used to analyze the motion of objects. However, in this problem, since the ring is balanced and not accelerating vertically, the equation F = ma is not directly relevant.
B. F = mg: This equation represents the force of gravity acting on an object, where m is the mass of the object and g is the acceleration due to gravity. This equation is used to calculate the weight of an object. In this problem, the forces F1 and F2 acting on the ring are due to weights hanging from pulleys. So, the equation F = mg is relevant to calculate the magnitudes of F1 and F2.
C. Fg = Fsin(theta): This equation represents the component of the force of gravity acting along a tilted surface, given the angle theta. In this problem, theta1 represents the angle between the vertical and the force F1. Since F1 is a weight hanging from a pulley, the force F1 can be resolved into its vertical component using this equation. Therefore, this equation is used in the derivation of the expected value of theta2.
D. Fg = Fcos(theta): This equation represents the component of the force of gravity acting perpendicular to a tilted surface, given the angle theta. In this problem, theta1 represents the angle between the vertical and the force F1. Since F1 is a weight hanging from a pulley, the force F1 can be resolved into its horizontal component using this equation. Therefore, this equation is used in the derivation of the expected value of theta2.
From the analysis above, the equation not used in the derivation is A. F = ma, as it is not directly relevant to the balanced forces acting on the ring in this vertical equilibrium problem.