Everything but vacuuming and golfing with a powered cart
The law applied here is Hooke's Law which describes the force exerted by the spring with a given distance. The equation for this is F = kΔx, where F is the force in Newtons, k is the spring constant in N/m while Δx is the displacement in meters.
If you want to find work done by a spring, this can be solved by using differential equations. However, derived equations are already ready for use. The equation is
W = k[{x₂-x₁)² - (x₁-xn)²],
where
xn is the natural length
x₁ is the stretched length
x₂ is also the stretched length when stretched even further than x₁
In this case xn =x₁. So, that means that (x₁-xn) = 0 and (x₂-x₁) = 11 cm or 0.11 m.
Then, substituting the values,
2 J = k (0.11² -0²)
k = 165.29 N/m
Finally, we use the value of k to the Hooke's Law to determine the Force.
F = kΔx = (165.29 N/m)(0.11 m)
F = 18.18 Newtons
To find the center of mass of an irregular shape using
String- for hanging at the center
• A small mass - hung from the string
• A stand-holding up the string
• A pencil pinpointing the center
• A straight-edge- Identify the middle
<h3>What is the center of mass?</h3>
Generally, a point indicates the mean location of the matter in a body or system.
In conclusion, the center of mass also indicates a point at which the body is most balanced under gravity.
Read more about the center of mass
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The individual directions of motion of Chirpy and Milada are components of projectile motion. A projectile motion is characterized by a motion in the shape of an arc. The thing about projectile motion is, the horizontal component and the vertical component are independent of each other. The horizontal motion acts on constant velocity, while the vertical motion acts on a constant acceleration equal to the force of gravity, 9.81 m/s². Even though they are independent, there is a relationship between them called the trajectory of a projectile equation:
y = xtanθ + gx²/2v²cos²θ
where
y is the vertical height
x is the horizontal range
θ is the angle of inclination
g is 9.81 m/s²
v is the initial velocity
Since Milada jumps horizontally, there is no angle of inclination: θ=0°. The initial velocity is equal to 95 cm/s or 0.95 m/s. Now, we have to determine x. But we can't do that without finding y first. This can be obtained from Chirpy's downward motion. In a free falling motion, the time of flight is equal to
t = √2y/g
2.70 = √2y/9.81
y = 35.757 m
Now, we can solve for x. I suggest you use your scientific calculator so that you can easily solve for x.
35.757 = xtan0° + (9.81)x²/2(0.95)²cos²0°
x = 2.565
Therefore, Melinda hits the ground 2.565 meters away from the base of the cliff.
Coulomb's Law
Given:
F = 3.0 x 10^-3 Newton
d = 6.0 x 10^2 meters
Q1 = 3.3x 10^-8 Coulombs
k = 9.0 x 10^9 Newton*m^2/Coulombs^2
Required:
Q2 =?
Formula:
F = k • Q1 • Q2 / d²
Solution:
So, to solve for Q2
Q2 = F • d²/ k • Q1
Q2 = (3.0 x 10^-3 Newton) • (6.0 x 10^2 m)² / (9.0 x 10^9
Newton*m²/Coulombs²) • (3.3x 10^-8 Coulombs)
Q2 = (3.0 x 10^-3 Newton) • (360 000 m²) / (297 Newton*m²/Coulombs)
Q2 = 1080 Newton*m²/ (297 Newton*m²/Coulombs)
Then, take the reciprocal of the denominator and start
multiplying
Q2 = 1080 • 1 Coulombs/297
Q2 = 1080 Coulombs / 297
Q2 = 3.63636363636 Coulombs
Q2 = 3.64 Coulumbs