The tension in the cable is 23.2 N
<h3>What is the tension in the string?</h3>
The tension in the cable can be resolved into horizontal and vertical forces Tcosθ and Tsinθ respectively.
Tcosθ, is acting perpendicularly, Tcosθ = 0
Taking moments about the pivot:
Tsinθ * 2.2 = 4 * 9.8 * 0.7
Solving for θ;
θ = tan⁻¹(1.4/2.2) = 32.5°
T = 27.44/(sin 32.5 * 2.2)
T = 23.2 N
In conclusion, the tension in the cable is determined by taking moments about the pivot.
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Answers:
a) 5400000 J
b) 45.92 m
Explanation:
a) The kinetic energy
of an object is given by:

Where:
is the mass of the train
is the speed of the train
Solving the equation:

This is the train's kinetic energy at its top speed
b) Now, according to the Conservation of Energy Law, the total initial energy is equal to the total final energy:


Where:
is the train's initial kinetic energy
is the train's initial potential energy
is the train's final kinetic energy
is the train's final potential energy, where
is the acceleration due gravity and
is the height.
Rewriting the equation with the given values:

Finding
:
Answer:
A. when the mass has a displacement of zero
Explanation:
The velocity of a mass on a spring can be calculated by using the law of conservation of energy. In fact, the total energy of the mass-spring system is equal to the sum of the elastic potential energy (U) of the spring and the kinetic energy (K) of the mass:

where
k is the spring constant
x is the displacement of the mass with respect to the equilibrium position of the spring
m is the mass
v is the velocity of the mass
Since the total energy E must remain constant, we can notice the following:
- When the displacement is zero (x=0), the velocity must be maximum, because U=0 so K is maximum
- When the displacement is maximum, the velocity must be minimum (zero), because U is maximum and K=0
Based on these observations, we can conclude that the velocity of the mass is at its maximum value when the displacement is zero, so the correct option is A.
is the intensity of the sound.
Answer: Option B
<u>Explanation:</u>
The range of sound intensity that people can recognize is so large (including 13 magnitude levels). The intensity of the weakest audible noise is called the hearing threshold. (intensity about
). Because it is difficult to imagine numbers in such a large range, it is advisable to use a scale from 0 to 100.
This is the goal of the decibel scale (dB). Because logarithm has the property of recording a large number and returning a small number, the dB scale is based on a logarithmic scale. The scale is defined so that the hearing threshold has intensity level of sound as 0.

Where,
I = Intensity of the sound produced
= Standard Intensity of sound of 60 decibels = 
So for 19 decibels, determine I as follows,



When log goes to other side, express in 10 to the power of that side value,


5
if zero falls between two significant numbers it becomes significant.