Reference no: EM13986314
Problem A new type of chair for a ski lift has been developed, and the manufacture has designed a simplified model (Figure) of chair's behavior upon loading a group of individuals.
Recall that the basic spring equation is:
W = k.x
where W is the weight or force applied to the spring, k is the spring constant, and x is the displacement (or stitch) of the spring.
You have been hired to calculate the total displacement of the system of springs and weights shown in Figure. The properties of the system are:
| Parameter |
Value |
| k1 |
10,000.0 N.m |
| k2 |
5,000.0 N.m |
| k3 |
8,000.0 N.m |
| k4 |
3,500.0 N.m |
| k5 |
4,500.0 N.m |
| W1 |
500.0 N |
| W2 |
1,000.0 N |
| W3 |
1,000.0 N |
The first step is to derive a force balance on each weight. For the first weight, WI, you need to consider every spring touching the weight, including the displacement and direction of force:
W1 = k1.x1 - k3.(x2 - x1) and for the second weight:
W2 = k2.x2 + k3.(X2 - X1) - k4.(X3 - X2) -k5.(X3 - X2)
In addition to the basic set of parameters given in the problem statement, the manufacturer has also asked you to include a plot of the displacement of each weight (i.e., each skier) as a function of W3. The plot should have a range of values for W3 on the x-axis, and then three curves showing the displacement (on the y-axis) of the different weights. You are free to use any linear system solver from chapter 6, including the solvers that are part of the SciPy and/or numpy packages.
|
Find the ball maximum height above the ground
: A boy reaches out of a window and tosses a ball straight up with a speed of 13m/s . The ball is 23m above the ground as he releases it. Use energy to find the ball's maximum height above the ground. Express your answer to two significant figures and..
|
|
What is breakeven point in units of production
: The annual fixed costs for a plant are$100,000.For production at 80% of the full capacity, the variable cost is$140,000 and the net sales is $280,000 if the selling price per unit is $40 Draw the breakeven chart. what is breakeven point in units of p..
|
|
What is the tension in the erector muscle
: What is the tension in the erector muscle? Hint: Align your x-axis with the axis of the spine. Express your answer to two significant figures and include the apporpriate units.
|
|
What are position, height, and orientation of final image
: A 1.0cm tall object is 5.0 cm in front of a converging lens with fL = +10.0 cm. Behind the lens, at a distance of 10.0 cm, is a concave mirror with a focal length fM = +30.0 cm. What are the position, height, and orientation of the final image?
|
|
Calculate the total displacement of the system of springs
: Calculate the total displacement of the system of springs - You are free to use any linear system solver from chapter 6, including the solvers that are part of the SciPy and/or numpy packages.
|
|
Describe what you think would be an effective new business
: Strategic, and structural levels of control. In what ways will your new approach to control be effective in the company's current environment?
|
|
What is the volume of the bubble as it reaches the surface
: A 1.0cm3 air bubble is released from the sandy bottom of a warm, shallow sea, where the gauge pressure is1.2atm . The bubble rises slowly enough that the air inside remains at the same constant temperature as the water. What is the volume of the b..
|
|
Can you recognize the aesthetic quality in the work
: Interpretation Follow your analysis with a subjective interpretation of the meaning of the work. How does the work make you feel? What do you think the content is? Go beyond "I like it" or "I don't like it."
|
|
Economic activity on both a domestic and global scale
: How do government policies and/or regulations factor into changes in economic activity on both a domestic and global scale? Give a specific example of a policy or regulation that has helped economic activity.
|