Answer questions 9-14 based on the graph (Mass is 5 kg) a: What is the value of
ID: 1645632 • Letter: A
Question
Answer questions 9-14 based on the graph (Mass is 5 kg)
a: What is the value of the positon of the mass when force is a maximum and positive? What values do the accelration and velocity have when this occur?
b: What is the value of the positon of the mass when force is a maximum and negative? What values do the accelration and velocity have when this occur?
c: What is the value of the positon of the mass when force is zero? What values do the accelration and velocity have when this occur?
d: What is the value of the positon of the mass when the kinetic energy is maximum? What is the potential energy there?
e: At what values of the position of the mass will the kinetic and potential energies be equal? Justify answer using the graphs.
5. Below is the position graph for a 5kg mass Hanging nU oCI simple harmonic motion similar to what we plotted in lab. On the axes provided, sketch the velocity, acceleration and force graphs. (You may use a ruler to draw in vertical lines to guide you.) 25 20 15 10 5 9 10 2 3 5 7 8 time (see)Explanation / Answer
Answer for (a):
For a spring mass system, force F= Kx, where is k= sprink constant and x= displacement of the mass from the mean position under the force (F).
From the above relation, force is directly proportional to displacement i.e Force maximum, for the maximum dispalcement from the mean position.
Mean position is the calculated as the average value of minimum to maximum displacement value. For the graph shown in above, the mean position value is located at "10cm" on the Y- axis.
For the force to be maximum and positive, the position values will be towards the side of maximum values from the mean position, which can be located at 20 cm at 1.5sec, 4.5sec, 7.5 sec, and so on.
In the spring mass system, the mass comes to rest at maximum position values. SO both velocity and acceleration become Zero at maximum positive force positions.
Answer for (b):
For the force to be maximum and negative, the position values will be towards the side of minimum values from mean values, which can be located at 0 cm at 0 sec, 3sec, 6 sec, and so on....
In this, again the mass comes to rest at manimum position. SO both velocity and acceleration become Zero at maximum neagative force positions.
Answer for (c):
The mean position (10 cm point on position axis) force acting on the mass is Zero. At this point velocity is maximum and acceleration is Zero.
Answer for (d):
Since the velocity is maximum at the mean position (10 cm point on position axis), the kinetic energy is also maximum at the same point. At the point, where the kinetice energy is maximum, potential energy is minimum or Zero.