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3 years ago

How do you find the slope of a force-extension graph?

1 answer:

3 0

The relationship between force and extension is a linear one, which means that if you plot a force vs. extension graph, you'll get a straight line. It will pass through the origin (x = 0; F = 0), and its slope will be equal to the spring constant, k.

Measure the Slope of the Force Extension Graph

In general, you can find the slope of a line by choosing two points and forming a ratio of the rise and the run between these two points. If the first point you choose is (x1, F1), and the second point is (x2, F2), the slope of the line is:

slope= f(2)- f(1)

---------

x(2)-x(1)

Assuming F2 is larger than F1.

This is the value of the spring constant, k. Despite the minus sign in the Hooke's law equation, k is a positive number, because the slope in the Hooke's law graph is positive.

Note that the spring constant has units of force/distance. In the MKS system, the spring constant units are newtons/meter. In the CGS system, they are dynes/centimeter. In the imperial system, they are pounds of force (lbf) /foot.

Now that you have the spring constant, you can predict exactly how much the spring will distend or compress when you subject it to any force.

You might be interested in

what are the common elements that make up series and parallel circuits , and how are circuits diagrammed?

Ahat [919]

<h2>Answer:</h2>

A series circuit occurs when the elements are connected along a simple path so the same current flows through all the elements. On the other hand, a parallel circuit occurs when there are two or more paths for the electricity to flow. The diagram are shown in the Figure below. We have chosen a source and resistors to illustrate this problem.

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3 years ago

An object with velocity 141 ft/s has a kinetic energy of 1558.71 ftâˆ™lbf, on a planet whose gravity is 31.5 ft/s2. What is its

Sidana [21]

Answer:

The mass of the object is 5.045 lbm.

Explanation:

Given;

kinetic energy of the object, K.E = 1558.71 ft.lbf

velocity of the object, V = 141 ft/s

The kinetic energy of the object is calculated as;

$K.E = \frac{1}{2} mV^2\\\\mV^2 = 2K.E\\\\m = \frac{2K.E}{V^2} \\\\1 \ lbf = 32.174 \ lbm.ft/s^2\\\\m = \frac{2 \ \times \ 1558.71 \ ft.lbf \ \times \ 32.174 \ lbm.ft/s^2 }{(141 \ ft/s)2 \ \ \times \ \ \ \ 1 \ lbf\ }$

$m = \frac{(2 \ \times \ 1558.71 \ \times \ 32.174) \ lbm.ft^2/s^2 }{(141 )^2\ ft^2/s^2 }\\\\m = \frac{(2 \ \times \ 1558.71 \ \times \ 32.174) \ lbm }{(141 )^2 }\\\\m = 5.045 \ lbm$

Therefore, the mass of the object is 5.045 lbm.

6 0

3 years ago

If you can throw a stone straight up to height h, what’s the maximum horizontal distance you could throw it over level ground?

Mariana [72]

To answer this question, first we take note that the maximum height that can be reached by an object thrown straight up at a certain speed is calculated through the equation,
Hmax = v²sin²θ/2g
where v is the velocity, θ is the angle (in this case, 90°) and g is the gravitational constant. Since all are known except for v, we can then solve for v whichi s the initial velocity of the projectile.

Once we have the value of v, we multiply this by the total time traveled by the projectile to solve for the value of the range (that is the total horizontal distance).

8 0

3 years ago

Read 2 more answers

. A spring has a length of 0.200 m when a 0.300-kg mass hangs from it, and a length of 0.750 m when a 1.95-kg mass hangs from it

kap26 [50]

Answer:

29.4 N/m

0.1

Explanation:

a) From the restoring Force we know that :

F_r = —k*x

the gravitational force :

F_g=mg

Where:

F_r is the restoring force .

F_g is the gravitational force

g is the acceleration of gravity

k is the constant force

xi , x2 are the displacement made by the two masses.

Givens:

m1 = 1.29 kg

m2 = 0.3 kg

x1 = -0.75 m

x2 = -0.2 m

g = 9.8 m/s^2

Plugging known information to get :

F_r =F_g

-k*x1 + k*x2=m1*g-m2*g

k=29.4 N/m

b) To get the unloaded length 1:

l=x1-(F_1/k)

Givens:

m1 = 1.95kg , x1 = —0.75m

Plugging known infromation to get :

l= x1 — (F_1/k)

= 0.1

3 0

3 years ago

Webster's defines a democracy as "a government by the people, especially: rule of the majority. A government in which the suprem

Lilit [14]

Answer:

Option A is correct

Explanation:

-The ten amendment was proposed for the sole purpose of protecting the minority from the brute greed of the majority.

- people established democratic government to protect the right, interest and welfare of the common people.

- The electoral college was designed for the sole purpose of protecting the minority interest and prevent special interest which is not in the public interest during electoral processes.

8 0

3 years ago