Answer:
k = 1073.09 N/m
A = 0.05 m
Explanation:
Given:
- Time period T = 0.147 s
- maximum speed V_max = 2 m/s
- mass of the block m = 0.67 kg
Find:
- The spring constant k
- The amplitude of the motion A.
Solution:
- A general simple harmonic motion is modeled by:
x (t) = A*sin(w*t)
- The velocity of the above modeled SHM is:
v = dx / dt
v(t) = A*w*cos(w*t)
- Where A is the amplitude in meters, w is the angular speed rad/s and time t is in seconds.
- We can see that maximum velocity occurs when (cos(w*t)) maximizes i.e it is equal to 1 or -1. Hence,
- V_max = A*w
- Where w is related to mass of the object and spring constant k as follows,
w = sqrt ( k / m )
- The relationship between w angular speed and Time period T is:
w = 2*pi / T
- Equating the above two equations we have,
m*(2*pi / T)^2 = k
- Hence, k = 0.67*(2*pi / 0.157)^2
k = 1073.09 N / m
- So, amplitude A is:
A = V_max*sqrt ( m / k )
A = 2*sqrt ( 0.67 / 1073.09 )
A = 0.05 m
Answer:
The slopes shows that the direction of the field is from -2 to +2, with three point charges, q₁, q₂ and q₃ at -2, 0 and +2 respectively.
Explanation:
Given;
The slope, dy/dx = 2x(y-6) - 4
2x(y-6) - 4 = 2xy - 12x - 4, divide through by 'x'
dy/dx = 2y -12 - 4/x
The slopes of the linear elements on the lines, x =0, y = 5, y = 6, y = 7.
At x = 0, and y = 5
dy/dx = 2y -12 - 4/x
dy/dx = 2(5) - 12 = -2
At x = 0, and y = 6
dy/dx = 2y -12 - 4/x
dy/dx = 2(6) - 12 = 0
At x = 0, and y = 7
= 2y -12 - 4/x
dy/dx = 2(7) - 12 = 2
Therefore, the slopes shows that the direction of the field is from -2 to +2, with three point charges, q₁, q₂ and q₃ at -2, 0 and +2 respectively.
The displacement of the object that moved 4 meters north, then 3 meters east is 5 meters.
<h3>
What is displacement?</h3>
Displacement is change in the position of an object. It can be described as the shortest distance between the initial and final position of an object.
The displacement of the object is calculated as follows;
d² = 4² + 3²
d² = 25
d = 5 m
Thus, the displacement of the object that moved 4 meters north, then 3 meters east is 5 meters.
Learn more about displacement here: brainly.com/question/2109763
#SPJ2
The mass of the object doesn't matter. The change in its momentum is equal to the impulse that changed it ... 15 N-sec.
