Answer:
W = 30 J
Explanation:
given,
Work done = 10 J
Stretch of spring, x = 0.1 m
We know,
dW = F .dx
we know, F = k x
![W = k[\dfrac{x^2}{2}]_0^{0.1}](https://tex.z-dn.net/?f=W%20%3D%20k%5B%5Cdfrac%7Bx%5E2%7D%7B2%7D%5D_0%5E%7B0.1%7D)
k = 2000
now, calculating Work done by the spring when it stretched to 0.2 m from 0.1 m.
![W = 2000 [\dfrac{x^2}{2}]_{0.1}^{0.2} dx](https://tex.z-dn.net/?f=W%20%3D%202000%20%5B%5Cdfrac%7Bx%5E2%7D%7B2%7D%5D_%7B0.1%7D%5E%7B0.2%7D%20dx)
W = 1000 x 0.03
W = 30 J
Hence, work done is equal to 30 J.
How can one explain<span> and predict the </span>interactions between objects<span> and within a system of </span>objects<span>? ... through </span>electric or magnetic fields to illustrate the forces between objects and the changes in energy of the objects due to the interaction<span>. ... </span>Forces<span> at a distance are </span>explained<span> by fields (gravitational, </span>electric<span>, and magnetic) ...</span>
<h2>K.E/P.E = m/k tan²φ x ω²</h2>
Explanation:
The given position of block x = x₀ cos(ωt + φ)
The velocity of block v = dx/dt = - x₀ sin(ωt + φ) x ω
The kinetic energy = 1/2 mv² = 1/2 m x₀² sin²(ωt + φ) x ω²
The potential energy of spring = 1/2 k x² , where k is the spring constant
Thus P.E = 1/2 x k x x₀² cos²(ωt + φ)
When t = 0
K.E = 1/2 m x₀²sin²φ x ω²
P.E = 1/2 k x₀² cos²φ
Dividing these , we have
K.E/P.E = m/k tan²φ x ω²
Answer:
Final velocity of NFL line backer is 16.67 m/s.
Explanation:
From the question, we have following data about the NFL line backer:
Initial Speed of line backer = Vi = 0 m/s (Since, he starts from rest)
Distance covered by NFL line backer = s = 100 m
Time taken by the NFL line backer to complete 100 m sprint = t = 12 s
Acceleration of NFL line backer during sprint = a
Final Velocity of NFL line backer = Vf = ?
First we need to find the acceleration of the NFL line backer. For that purpose we will use 2nd equation of motion:
s = (Vi)(t) + (0.5)at²
using values:
100 m = (0 m/s)(12 s) + (0.5)(a)(12 s)²
100 m/72 s² = a
a = 1.39 m/s²
Now, we use 1st equation of motion to find Vf:
Vf = Vi + at
Vf = 0 m/s + (1.39 m/s²)(12 s)
<u>Vf = 16.67 m/s</u>
Answer:
64,000 centimeters =640 meters
