Let denote the angle made by a given force with the positive <em>x</em>-axis (pointing right). So in (1), <em>A</em> makes an angle of 90º - 30º = 60º, and <em>B</em> makes an angle of -45º; and in (2), <em>A</em> still makes angle of 30º, <em>B</em> makes an angle of -15º, and <em>C</em> makes one of -90º.
Separate each force vector in to <em>x</em>- and <em>y</em>-components, then compute the required vector. This involves writing each given vector as
where
(1)
(2)
Answer:
<em>The tension force of the cable is 588 N</em>
Explanation:
<u>Net Force</u>
The Second Newton's law establishes that the acceleration an object has depends on the net force through the equation:
F = m.a
If the net force is zero, then the acceleration is zero, and the object's velocity remains constant.
The crane lifts a 60 Kg load at a constant velocity. It means the net force acting on the load is zero.
There are two forces acting on the load: The weight of the load and the tension of the cable that holds it.
Since the net force is zero, both forces have the same magnitude:
T=588 N
The tension force of the cable is 588 N
(1) You must find the point of equilibrium between the two forces,
<span>G * <span><span><span>MT</span><span>ms / </span></span><span>(R−x)^2 </span></span>= G * <span><span><span>ML</span><span>ms / </span></span><span>x^2
MT / (R-x)^2 = ML / x^2
So,
x = R * sqrt(ML * MT) - ML / (MT - ML)
R = is the distance between Earth and Moon.
</span></span></span>The result should be,
x = 3.83 * 10^7m
from the center of the Moon, and
R - x = 3.46*10^8 m
from the center of the Earth.
(2) As the distance from the center of the Earth is the number we found before,
d = R - x = 3.46*10^8m
The acceleration at this point is
g = G * MT / d^2
g = 3.33*10^-3 m/s^2
There's no way we can calculate how much the springs will stretch, because we don't know their "spring constants" ... how far 1 Newton of force will stretch each spring.
But we do know that both springs will stretch the same amount, because they're identical and they share the load equally.
So ...
The weight of the load is (mass) x (gravity) = (0.25 kg) x (9.81 m/s²) = 2.4525N
Each spring supports half of the load = 1.22625 N
If ' k ' is the spring constant of each spring, then each spring stretches by
<em>1.2265/k meters</em> .
Answer:
Time taken by the coin to reach the ground is 1.69 s
Given:
Initial speed, v = 11.8 m/s
Height of the building, h = 34.0 m
Solution:
Now, from the third eqn of motion:
Now, time taken by the coin to reach the ground is given by eqn (1):
v' = v + gt