Concept explainers
When a block of mass M, connected to the end of a spring of mass ms = 7.40 g and force constant k, is set into
A two-part experiment is
(a)
To draw: The graph of
Answer to Problem 15.76AP
The graph of
Explanation of Solution
Given info: The block of mass is
The values of mass and the static extension are given and calculate the value of the
Static extension (x) in
| Mass (M) in
| Weight
|
0.17 | 0.02 | 0.196 |
0.293 | 0.04 | 0.392 |
0.353 | 0.05 | 0.49 |
0.413 | 0.06 | 0.588 |
0.471 | 0.07 | 0.686 |
0.493 | 0.08 | 0.784 |
Table (1)
Conclusion:
The table (1) indicates the values required to plot the graph of
Figure (1)
(b)
The value of
Answer to Problem 15.76AP
The value of
Explanation of Solution
Given info: The block of mass is
The equation of the graph is,
The slope intercept form of the equation of the line is,
Here,
Compare equation (1) and (2).
Since the slope of the graph indicates the force constant of the spring.
Conclusion:
Therefore, the value of
(c)
To draw: The table of given masses and the times.
Answer to Problem 15.76AP
The table of given masses and the times is,
Mass in
| Time intervals in
|
20 | 7.03 |
40 | 9.62 |
50 | 10.67 |
60 | 11.67 |
70 | 12.52 |
80 | 13.41 |
Explanation of Solution
Given info: The block of mass is
The values of mass and the static extension are given and calculate the value of the
Mass in
| Time intervals in
|
20 | 7.03 |
40 | 9.62 |
50 | 10.67 |
60 | 11.67 |
70 | 12.52 |
80 | 13.41 |
Table (2)
Conclusion:
The table (1) indicates the values of mass and the time intervals.
(d)
The experimental value for
Answer to Problem 15.76AP
The experimental values for
Explanation of Solution
Given info: The block of mass is
The expression for the time periods for each experiment is,
Here,
The ten experiments are conducted.
Calculate time periods for each experiment.
Total time period
| Time period for one experiment
|
7.03 | 0.703 |
9.62 | 0.962 |
10.67 | 0.1067 |
11.67 | 1.167 |
12.52 | 1.252 |
13.41 | 1.341 |
Table (3)
Conclusion:
Therefore, the experimental values for
(e)
To draw: The graph of
Answer to Problem 15.76AP
The graph of
Explanation of Solution
Given info: The block of mass is
Time period for one experiment
|
| Mass (M) in
|
0.703 | 0.494209 | 0.02 |
0.962 | 0.925444 | 0.04 |
0.1067 | 1.138489 | 0.05 |
1.167 | 1.361889 | 0.06 |
1.252 | 1.567504 | 0.07 |
1.341 | 1.798281 | 0.08 |
Table (4)
The table (4) indicates the values required to plot the graph of
Figure (2)
(f)
The value of
Answer to Problem 15.76AP
The value of
Explanation of Solution
Given info: The block of mass is
The equation of the graph is,
The given expression is,
Square both sides in above expression.
Compare equation (3) and (4).
Conclusion:
Therefore, the value of
(g)
The comparison in value of
Answer to Problem 15.76AP
The value of
Explanation of Solution
Given info: The block of mass is
The value of
The value of
Compare the values.
Conclusion:
Therefore, the value of
(h)
The value of
Answer to Problem 15.76AP
The value of
Explanation of Solution
Given info: The block of mass is
The equation of the graph is,
The given expression is,
Square both sides in above expression.
Compare both the above expression.
Substitute
Conclusion:
Therefore, the value of
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Chapter 15 Solutions
Physics for Scientists and Engineers, Volume 1
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