Two conducting spheres are each given a charge Q. The radius of the larger sphere is three times greater than that of the smalle
1 answer:
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The translational equilibrium condition allows finding that the response for cable length with a maximum tension is
L = 2.56 m
Newton's second law says that the force is proportional to the mass and the acceleration of the body, in the special case that the acceleration is zero, the relationship is called the translational equilibrium condition.
∑ F = 0
Where the bold indicates vectors, F is the force and the sum is for all external forces.
The reference systems are coordinate systems with respect to which the decomposition of the vectors is carried out and the measurements are made, in this case we will use a system with the horizontal x axis and the vertical y axis.
In the attachment we can see a free body diagram of the system, let's write the equilibrium condition for each axis.
x-axis
Tₓ -Tₓ = 0
y-axis
2 - W = 0
Let's use trigonometry to decompose the tension, we can see from the graph and the adjoint that each string is half the length, let's call the angle θ
cos θ =
sin θ =
Tₓ = T cos θ
= T sin θ
We substitute
2 T sin θ = W (1)
The text indicates that the length of the block is 2 m, so the distance to the midpoint is
x = 1 m
Let's use the Pythagoras' Theorem
H² = CA² + CO²
CO =
CA = x
CO =
Where CO is the opposite leg, CA is the adjacent leg and H is the hypotenuse indicating H = L / 2,
Let's write the trigonometry functions
sin θ =
Let's substitute
sin θ =
Let's subtitute in the equation 1
2 T ( \frac{2 \sqrt{\frac{L^2}{4} -1 } }{L} ) = W
Let's solve by squaring
They indicate that the maximum tension of the cable is T = 700N and the weight is worth W = 700N, we substitute the values
L = 2.31 m
In conclusion using the translational equilibrium condition we can find that the response for cable length with maximum tension is
L = 2.31 m
Learn more about translational equilibrium here:
Answer:
the ratio of Hank's mass to Harry's mass is 0.7937 or [ 0.7937 : 1
Explanation:
Given the data in the question;
Hank and Harry are two ice skaters, since both are on top of ice, we assume that friction is negligible.
We know that from Newton's Second Law;
Force = mass × Acceleration
F = ma
Since they hold on to opposite ends of the same rope. They have the same magnitude of force |F|, which is the same as the tension in the rope.
Now,
Mass × Acceleration
= Mass
× Acceleration
so
Mass / Mass
= Acceleration
/ Acceleration
given that; magnitude of Hank's acceleration is 1.26 times greater than the magnitude of Harry's acceleration,
Mass / Mass
= 1 / 1.26
Mass / Mass
= 0.7937 or [ 0.7937 : 1 ]
Therefore, the ratio of Hank's mass to Harry's mass is 0.7937 or [ 0.7937 : 1 ]