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iVinArrow [24]
3 years ago
5

A mass m attached to a horizontal massless spring with spring constant k, is set into simple harmonic motion. its maximum displa

cement from its equilibrium position is
a. what is the masses speed as it passes through its equilibrium position?
Physics
1 answer:
Lesechka [4]3 years ago
6 0
At the point of maximum displacement (a), the elastic potential energy of the spring is maximum:
U_i= \frac{1}{2} ka^2
while the kinetic energy is zero, because at the maximum displacement the mass is stationary, so its velocity is zero:
K_i =0
And the total energy of the system is
E_i = U_i+K= \frac{1}{2}ka^2

Viceversa, when the mass reaches the equilibrium position, the elastic potential energy is zero because the displacement x is zero:
U_f = 0
while the mass is moving at speed v, and therefore the kinetic energy is
K_f =  \frac{1}{2} mv^2
And the total energy is
E_f = U_f + K_f =  \frac{1}{2} mv^2

For the law of conservation of energy, the total energy must be conserved, therefore E_i = E_f. So we  can write
\frac{1}{2} ka^2 =  \frac{1}{2}mv^2
that we can solve to find an expression for v:
v= \sqrt{ \frac{ka^2}{m} }
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6 0
2 years ago
A 600 kg car is at test and then accelerated to 5m/s , what is its original kinetic energy
ycow [4]

Answer:

0 J

Explanation:

Kinetic energy is defined as:

KE = 1/2 m v²

where m is mass and v is velocity.

The car starts at rest, so it has zero velocity.  Therefore, its initial kinetic energy is 0 J.

3 0
3 years ago
For sprinters running at 12 m/s around a curved track of radius 26 m, how much greater (as a percentage) is the average total fo
Snezhnost [94]

Answer:

114.86%

Explanation:

In both cases, there is a vertical force equal to the sprinter's weight:

Fy = mg

When running in a circle, there is an additional centripetal force:

Fx = mv²/r

The net force is found with Pythagorean theorem:

F² = Fx² + Fy²

F² = (mv²/r)² + (mg)²

F² = m² ((v²/r)² + g²)

F = m √((v²/r)² + g²)

Compared to just the vertical force:

F / Fy

m √((v²/r)² + g²) / mg

√((v²/r)² + g²) / g

Given v = 12 m/s, r = 26 m, and g = 9.8 m/s²:

√((12²/26)² + 9.8²) / 9.8

1.1486

The force is about 114.86% greater (round as needed).

5 0
3 years ago
A 0.200-kg cube of ice (frozen water) is floating in glycerine.The gylcerine is in a tall cylinder that has inside radius 3.90 c
natita [175]

Answer:

Part a)

h = 0.86 cm

Part b)

Level will increase

Explanation:

Part a)

Mass of the ice cube is 0.200 kg

Now from the buoyancy force formula we know that weight of the ice is counter balanced by buoyancy force on the ice

So here we will have

mg = \rho V_{displaced} g

V_{displaced} = \frac{m}{\rho}

V_{displaced} = \frac{0.200}{1260} = 1.59 \times 10^{-4} m^3

now as we know that ice will melt into water

so here volume of water that will convert due to melting of ice is given as

V\rho_w = m_{ice}

V = \frac{0.200}{1000} = 2\times 10^{-4} m^3

So here extra volume that rise in the level will be given as

\Dleta V = V - V_{displaced}

\pi r^2 h = 2\times 10^{-4} - 1.59 \times 10^{-4}

(\pi (0.039^2) h = 0.41 \times 10^{-4}

h = 0.86 cm

Part b)

Since volume of water that formed here is more than the volume that is displaced by the ice so we can say that level of liquid in the cylinder will increase due to melting of ice

5 0
4 years ago
The velocity of a wave is 500 m/s . The wavelength of the wave is 3.2 m . What is the frequency of the wave ?
nasty-shy [4]

Answer:

f=156.25Hz

Explanation:

v=fT

500=fx3.2

500=3.2f

divide both sides by 3.2

f=156.25Hz

6 0
3 years ago
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