Ask question

Ask question

All categories

1 year ago

10

If we double only the amplitude of a vibrating ideal mass-and-spring system, the mechanical energy of the system:

1 answer:

Lelechka [254]1 year ago

8 0

Answer:

D. increases by a factor of 4.

Explanation:

General equation of SHM

Lets taken the general equation of the displacement given as

x = A sinω t

A=Amplitude ,t=time ,ω=natural frequency

We know that speed V

$V=\dfrac{dx}{dt}$

V= A ω cosωt

The mechanical energy of spring mass system

$U=\dfrac{1}{2}KA^2$

K=Spring constant

Now when Amplitude A become 2 times then the mechanical energy will become 4 times.

Therefore the answer is D.

You might be interested in

A giant wall clock with diameter d rests vertically on the floor. The minute hand sticks out from the face of the clock, and its

Katyanochek1 [597]

Answer:

$d_{x}(t)=(D/2)cos(\frac{\pi}{30}*t)$

Explanation:

We can try writing the equation of the horizontal component of the length of the minute hand in terms of distance and the angle, that depends of time in this particular case.

The x-component of the length of the minute hand is:

$d_{x}(t)=dcos(\theta (t))$ (1)

d is the length of the minute hand (d=D/2)
D is the diameter of the clock
t is the time (min)

Now, using the angular kinematic equations we can express the angle in term of angular velocity and time. As we know, the minute hand moves with a constant angular velocity, so we can use this equation:

$\theta (t)=\omega *t$ (2)

Also we know, that the minute hand moves 90 degrees or π/2 rad in 15 min, so using the definition of angular velocity, we have:

$\omega=\frac{\Delta \theta}{\Delta t}=\frac{\theta_{f}-\theta_{i}}{t_{f}-t{i}}=\frac{\pi/2-0}{15-0}=\frac{\pi}{30}$

Now, let's put this value on (2)

$\theta (t)=\frac{\pi}{30}*t$

Finally the length x(t) of the shadow of the minute hand as a function of time t, will be:

$d_{x}(t)=(D/2)cos(\frac{\pi}{30}*t)$

I hope it helps you!

6 0

1 year ago

A lever has a 36cm input arm and a 6cm output arm. find MA.

Nady [450]

6

Explanation:

The mechanical advantage is a factor that measures how input force increases using a machine.

A lever is a simple machine with the fulcrum at the center.

To calculate the mechanical advantage M.A of levers we use the expression below;

M. A = $\frac{F_{b} }{F_{a} }$ = $\frac{a}{b}$

$F_{a}$ = input force

$F_{b}$ = output force

a is the distance of the input force from the fulcrum

b is the distance of the output force from the fulcrum

Given

a = 36cm

b = 6cm

M.A = $\frac{36cm}{6cm}$ = 6

learn more:

Torque brainly.com/question/5352966

#learnwithBrainly

6 0

1 year ago

A block rests on a flat plate that executes vertical simple harmonic motion with a period of 0.74 s. What is the maximum amplitu

Mumz [18]

Answer:

maximum amplitude = 0.13 m

Explanation:

Given that

Time period T= 0.74 s

acceleration of gravity g= 10 m/s²

We know that time period of simple harmonic motion given as

$T=\dfrac{2\pi}{\omega}$

$0.74=\dfrac{2\pi}{\omega}$

ω = 8.48 rad/s

ω=angular frequency

Lets take amplitude = A

The maximum acceleration given as

a= ω² A

The maximum acceleration should be equal to g ,then block does not separate

a= ω² A

10= 8.48² A

A=0.13 m

maximum amplitude = 0.13 m

8 0

1 year ago

Caelyn wanted to find out what shampoo made her hair the shiniest . Everyday she washed her hair with different shampoos and the

Arte-miy333 [17]

Answer:

IV: type of shampoo used

DV: what shampoo made her hair the skinniest

control: water

Constant: rated from scale from 1-10

Explanation:

8 0

1 year ago

A group of students prepare for a robotic competition and build a robot that can launch large spheres of mass M in the horizonta

Dvinal [7]

Nobody will do that for 5 points loll

8 0

1 year ago