Reference no: EM132269994
Question 1
A 0.2kg mass is at rest on an inclined surface, which has an angle of inclination of 15 degrees. The surface has very low friction. A spring is attached to the mass at one end. Based on the free body diagram shown below, which of the following is a correct relationship to describe the spring force acting on the box?
- mg
- mgcos(θ)
- mgtan(θ)
- mgsin(θ)
Question 2
A 0.2kg mass is at rest on an inclined surface, which has an angle of inclination of 15 degrees. The surface has very low friction. A spring is attached to the mass at one end. What is the value of the spring force? (Put in a completely numerical answer that would have units of Newtons.)
Question 3
According to Hooke's Law, Fspring = -k Δx
You conduct an experiment in which a spring is stretched a variety of distances due to various forces. If you were to plot the force on the spring on the y-axis of a graph and the displacement of the spring on the x-axis of a graph, where would you theoretically expect the data to intersect the y-axis according to Hooke's Law?
Question 4
According to Hooke's Law, Fspring = -k Δx
You conduct an experiment in which a spring is stretched a variety of distances due to various forces. If you were to plot the force on the spring on the y-axis of a graph and the displacement of the spring on the x-axis of a graph, what would the slope of the line going through the data represent according to Hooke's Law?
Question 5
A scientist does the experiment described above. Their results are shown in a table and in a graph below.
|
x_initial (m)
|
x_final (m) |
Δx (m) |
m (kg) |
F (N) |
|
0.032
|
0.034
|
0.002
|
0.050
|
-0.4904
|
|
0.032
|
0.05
|
0.018
|
0.100
|
-0.9808
|
|
0.032
|
0.058
|
0.026
|
0.120
|
-1.17696
|
|
0.032
|
0.071
|
0.039
|
0.150
|
-1.4712
|
|
0.032
|
0.09
|
0.058
|
0.200
|
-1.9616
|
What is the spring constant of this spring?
- 9.8 N/m
- 0.4771 N/m
- 0.9966 N/m
- 25.807 N/m
Question 6
A scientist does the experiment described above. Their results are shown in a table and in a graph below.
|
x_initial (m)
|
x_final (m) |
Δx (m) |
m (kg) |
F (N) |
|
0.032
|
0.034
|
0.002
|
0.050
|
-0.4904
|
|
0.032
|
0.05
|
0.018
|
0.100
|
-0.9808
|
|
0.032
|
0.058
|
0.026
|
0.120
|
-1.17696
|
|
0.032
|
0.071
|
0.039
|
0.150
|
-1.4712
|
|
0.032
|
0.09
|
0.058
|
0.200
|
-1.9616
|
While Hooke's Law states that Fspring = -kΔx most springs still have some sort of "residual force' or 'internal force" within them. You must exert more than this amount of force to get the spring to stretch at all. Most springs follow a modified version of Hooke's Law that is modeled more like: Fspring = -kΔx -Fresidual.
Based on the data above. what do you believe is the "residual force" in this spring?
- 0.9966 N
- 9.8 N
- 0.4771 N
- 25.807 N
Question 7
You perform experiments to generate graphs as seen in the previous questions in order to extract the spring constant and residual force constant. In order to get error bars on these values, you perform a LINEAR REGRESSION.
This statistical test tells you the 95% confidence range (lower range value. upper range value) for the slope and y-intercept of the trend line on your graphs. The results are seen below for two different springs. Which of the following statements is true based on the data? Choose all that apply.
|
Spring A
|
|
Lower 95.0%
|
Upper 95.0%
|
|
Residual Force constant
|
Intercept
|
-0.572630657
|
-0.381594776
|
|
Spring constant
|
X Variable 1
|
-28.59047816
|
-23.02401717
|
|
Spring B
|
|
Lower 95.0%
|
Upper 95.0%
|
|
Residual Force constant
|
intercept
|
-0.415234123
|
-0.05735933
|
|
Spring constant
|
X Variable 1
|
-30.61867076
|
-22.01053751
|
It is possible that the true value for the spring constant of Spring A is 26 N/m.
The residual force constant of Spring A is within the range of 0.3816-0.5726 N.
The residual force constant of Spring B is within the range of 0.0574-0.4152 N.
The spring constant of Spring A is much lower than the spring constant of Spring B.
The residual force constant of Spring A does not agree with the residual force constant of Spring B. to a 95% confidence interval.