Answer:
k = 1400.4 N / m
Explanation:
When the springs are oscillating a simple harmonic motion is created where the angular velocity is
w² = k / m
w = 
where angular velocity, frequency and period are related
w = 2π f = 2π / T
we substitute
2π / T = \sqrt{ \frac{k}{m} }
T² = 4π² 
k = π² 
in this case the period is T = 1.14s, the combined mass of the children is
m = 92.2 kg and the constant of the two springs is
k = 4π² 92.2 / 1.14²
k = 2800.8 N / m
to find the constant of each spring let's use the equilibrium condition
F₁ + F₂ - W = 0
k x + k x = W
indicate that the compression of the two springs is the same, so we could replace these subtraction by another with an equivalent cosecant
(k + k) x = W
2k x = W
k_eq = 2k
k = k_eq / 2
k = 2800.8 / 2
k = 1400.4 N / m
Answer:
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We will apply the concepts related to Newton's second law. At the same time we will convert everything to the system of international units.
The values of the velocities are,
We know that the acceleration is equivalent to the change of the speed in a certain time therefore
Now applying the Newton's second law we have,
Therefore the approximate magnitude is 8516.36N
Answer:
A) a frictional force is acting on it
Explanation:
The crate is sliding down the inclined ramp at constant velocity: constant velocity means zero acceleration, a = 0. According to Newton's second law:
F = ma
this also means that the net force acting along the direction of the slope is zero.
Without frictional force, there would be only one force acting along this direction: the component of the weight of the crane parallel to the slope, acting downward:
where 
is the angle of the incline. Therefore, the net force along this direction would not be zero. In order to have a net force of zero, there must be another force acting upward on the crate: and the only force that is possibly acting on the crate against its direction of motion is the frictional force, whose magnitude must be equal to 
, in order to produce a net force of zero (and therefore, a zero acceleration).
