Which element could have the dot diagram shown below?

The maximum speed of a mass m on an oscillating spring is vmax . what is the speed of the mass at the instant when the kinetic a

umka21 [38]

Let
A = the amplitude of vibration
k = the spring constant
m = the mass of the object

The displacement at time, t, is of the form
x(t) = A cos(ωt)
where
ω = the circular frequency.

The velocity is
v(t) = -ωA sin(ωt)

The maximum velocity occurs when the sin function is either 1 or -1.
Therefore
$v_{max} = \omega A$
Therefore
$v(t) = -V_{max} sin(\omega t)$

The KE (kinetic energy) is given by
$KE = \frac{m}{2}v^{2} = \frac{m}{2} V_{max}^{2} sin^{2} (\omega t)$

The PE (potential energy) is given by
$PE = \frac{k}{2} x^{2} = \frac{k}{2} A^{2} cos^{2} (\omega t)$

When the KE and PE are equal, then
$v^{2} = \frac{k}{m} A^{2} cos^{2} (\omega t)$

For the oscillating spring,
$\omega ^{2} = \frac{k}{m} \\ V_{max} = \omega A = \sqrt{ \frac{k}{m} } A$
Therefore
$v^{2} = \frac{k}{m} \frac{m}{k} V_{max}^{2} cos^{2} ( \sqrt{ \frac{k}{m} t} ) \\ v = V_{max} \,cos( \sqrt{ \frac{k}{m} t} )$

Answer: $v(t) = V_{max} cos( \sqrt{ \frac{k}{m} t} )$

3 0

4 years ago

. An express train passes through a station. It enters with an initial velocity of 22.0 m/s and decelerates at a rate of 0.150 m

Alekssandra [29.7K]

Answer:

Explanation:

Give it that,

Initial velocity

u = 22m/s

Deceleration a = - 0.15m/s2

Time taken to travel a station long of 210m

Using equation of motion

Let know the final velocity, when it leaves the station

v² = u²+2as

v² = 22²+2×(-0.15)×210

v² = 484—63

v² = 421

v =√421

v = 20.52m/s

Then,

Using equation of motion to find time taken

v = u + at

20.52 = 22 +(-0.15)t

20.52-22 = -0.15t

-0.15t = -1.48

t = -1.48/-0.15

t = 9.88 sec

6 0

3 years ago

The displacement ‘x’of a particle is dependent on time ‘t’according to the relation X= 3 -5t +<img src="https://tex.z-dn.net/?f=

rusak2 [61]

Answer:

Explanation:

A.

8 0

3 years ago

Check the correctness of given equation

FromTheMoon [43]

Please find attached photograph for your answer. Hope it helps. Please do comment and mark me as brainliest.

5 0

3 years ago

He net force acting on an stationary object is zero. Which best describes the object’s velocity?

sergij07 [2.7K]

When the net force acting on an object is zero, its velocity is constant.
That means that the object is moving in a straight line with a speed that
doesn't change.

You said that the object is 'stationary'. That means that it's not moving.
So its speed and its velocity are both zero.

5 0

3 years ago