assuming the reference line to measure the height for gravitational potential energy lying at the equilibrium position
m = mass attached to the spring = 10.00 kg
k = spring constant of the spring = 250 N/m
h = height of the mass above the reference line or equilibrium position = 0.50 m
x = compression of the spring = 0.50 m
v = speed of mass = 2.4 m/s
A = maximum amplitude of the oscillation
v' = speed of mass at the maximum amplitude location = 0 m/s
using conservation of energy between the point where the speed is 2.4 m/s and the highest point at which displacement is maximum from equilibrium
kinetic energy + spring potential energy + gravitational potential energy = kinetic energy at maximum amplitude + spring potential energy at maximum amplitude + gravitational potential energy at maximum amplitude
(0.5) m v² + m g h + (0.5) k x² = (0.5) m v'² + m g A + (0.5) k A²
inserting the values
(0.5) (10) (2.4)² + (10) (9.8) (0.50) + (0.5) (250) (0.50)² = (0.5) (10) (0)² + (10) (9.8) A + (0.5) (250) A²
109.05 = (98) A + (125) A²
A = 0.62 m
Answer:
Explanation:
L 1: front radius 950 mm, rear radius 2700 mm, refractive index 1.528;
We shall use lens maker's formula , that is
1/f = (μ-1) ( 1/R₁ - 1/R₂) , μ is refractive index of the lens , R₁ and R₂ are radius of curvature of front and rear curved surface.
1/f₁ = (1.528-1)( 1/950 + 1/2700)
f₁ = 1331 mm
L2: front radius 535 mm, rear radius 500 mm, refractive index 1.550.
1/f₂ = (1.550-1)( 1/535 + 1/500)
f₂ = 470 mm
largest angular magnification possible
= f₁ /f₂
= 1331 / 470
= 2.83 ( approx )
Length between two lenses
=1331 +470
= 1801 mm
= 1.8 m Ans
Answer:
A skater glides along a circular path. She defines a certain point on the circle as her origin. Later on, she passes through a point at which the distance she has traveled along the path from the origin is smaller than the magnitude of her displacement vector from the origin.
So here in circular motion of the skater we can see that the total path length of the skater is along the arc of the circle while we can say that displacement is defined as the shortest distance between initial and final position of the object.
So it is not possible in any circle that arc-length is less than the chord joining the two points on the circle
As we know that arc length is given as
length of chord is given as
so here
so we have
Answer:
They transfered more energy in the morning.
Explanation:
This is because, let me put this in simple words, you have more energy, you can run more laps around the track, right? This is the same with the waves. They have more energy, so they can crash aganst the shore more!
Answer:
590 ohms
Explanation:
Let the resistance of each resistor be 'R'.
Given:
Equivalent resistance of the three resistors in parallel
Plug in the given values and solve for 'R'. This gives,
Now, the equivalent resistance of the three identical resistors in series is the sum of each of the resistors. Therefore,
As the question asks to round off to two significant figures, so we add 1 to the second significant figure because the number next to 8 is 5 which is greater than or equal to 5. So, the number becomes 590.
Hence, the equivalent resistance in series is 590 ohms.