There is an accident up the road from your car. You see other cars ahead of you. Who will stop first?
2 answers:
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Answer:
a)
b)
c)
d)
e)
Explanation:
1) Important concepts
Simple harmonic motion is defined as "the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law (F=-Kx). The motion experimented by the particle is sinusoidal in time and demonstrates a single resonant frequency".
2) Part a
The equation that describes the simple armonic motion is given by (1)
And taking the first and second derivate of the equation (1) we obtain the velocity and acceleration function respectively.
For the velocity:
(2)
For the acceleration
(3)
As we can see in equation (3) the acceleration would be maximum when the cosine term would be -1 and on this case:
Since we know the amplitude A=0.002m we can solve for like this:
And we with this value we can find the period with the following formula
3) Part b
From equation (2) we see that the maximum velocity occurs when the sine function is euqal to -1 and on this case we have that:
4) Part c
In order to find the total mechanical energy of the oscillator we can use this formula:
5) Part d
When we want to find the force from the 2nd Law of Newton we know that F=ma.
At the maximum displacement we know that X=A, and in order to that happens , and we also know that the maximum acceleration is given by::
So then we have that:
And since we have everything we can find the force
6) Part e
When the mass it's at the half of it's maximum displacement the term and on this case the acceleration would be given by;
And the force would be given by:
And replacing we have:
Answer:
The mechanical advantage of the system is equal to 19.62
Explanation:
The ratio of the force produced by a machine to the force applied to it is called mechanical advantage. In other words it is the ratio of output force to the input force.
In this problem mass=200kg
applied force=100N
input force=100N
output force=
mechanical advantage
It gives an idea about the efficiency of a mechanical device. It is indeed a measure of force amplification. In block and tackle system an assembly of ropes and pulleys is used to lift loads. When the moving block is supported by a greater number of rope sections the force amplification will be more.