Ask question

Ask question

All categories

2 years ago

11

A 0.750-kg object hanging from a vertical spring is observed to oscillate with a period of 1.50 s. When the 0.750-kg object is r

emoved and replaced by a 1.50-kg object, what will be the period of oscillation

1 answer:

lawyer [7]2 years ago

3 0

Answer:

New time period, $T_2=2.12\ s$

Explanation:

Given that,

Mass of the object 1, $m_1=0.75\ kg$

Time period, $T_1=1.5\ s$

If object 1 is replaced by object 2, $m_2=1.5\ kg$

Let $T_2$ is the new period of oscillation.

The time period of oscillation of mass 1 is given by :

$T_1=2\pi \sqrt{\dfrac{m_1}{k}}$

$1.5=2\pi \sqrt{\dfrac{0.75}{k}}$ ............(1)

The time period of oscillation of mass 2 is given by :

$T_2=2\pi \sqrt{\dfrac{m_2}{k}}$

$T_2=2\pi \sqrt{\dfrac{1.5}{k}}$ ............(2)

From equation (1) and (2) we get :

$(\dfrac{T_1}{T_2})^2=\dfrac{m_1}{m_2}$

$(\dfrac{1.5}{T_2})^2=\dfrac{0.75}{1.5}$

$\dfrac{1.5}{T_2}=0.707$

$T_2=2.12\ s$

So, the new period of oscillation is 2.12 seconds. Hence, this is the required solution.

You might be interested in

A mass spectrometer is being used to separate common oxygen-16 from the much rarer oxygen-18, taken from a sample of old glacial

Nataly_w [17]

Answer:

0.092 m

Explanation:

A charged moving particle immersed in a region with magnetic field follows a circular trajectory at constant speed (uniform circular motion), since the magnetic forces acts perpendicular to the direction of motion of the particle.

Since the magnetic force acts as centripetal force, we can write:

$qvB=m\frac{v^2}{r}$

where

q is the charge of the particle

v is its velocity

B is the strength of the magnetic field

m is the mass of the particle

r is the radius of the orbit

Solving the equation for r,

$r=\frac{mv}{qB}$

For the ion of oxygen-16, we have:

$m_A=2.66\cdot 10^{-26}kg$

$q_A = 1.6\cdot 10^{-19}C$ (it is singly charged)

$v_A=2.90\cdot 10^6 m/s$

$B_A=1.30 T$

So the radius of its orbit is

$r_A=\frac{m_A v_A}{q_A B_A}=\frac{(2.66\cdot 10^{-26})(2.90\cdot 10^6)}{(1.6\cdot 10^{-19})(1.30)}=0.371 m$

For the ion of oxygen-18, we have:

$m_B = \frac{18}{16}m_A = 2.99\cdot 10^{-26}kg$

$q_B = 1.6\cdot 10^{-19}C$ (it is singly charged)

$v_B=2.90\cdot 10^6 m/s$

$B_B=1.30 T$

So the radius of its orbit is

$r_B=\frac{m_B v_B}{q_B B_B}=\frac{(2.99\cdot 10^{-26})(2.90\cdot 10^6)}{(1.6\cdot 10^{-19})(1.30)}=0.417 m$

After each ion has travelled a semicircle, the separation between the two ions will be twice the difference in their radius, so:

$d=2(r_B-r_A)=2(0.417-0.371)=0.092 m$

3 0

2 years ago

An object is held at rest and allowed to drop How far does the object fall in 3.3 seconds?

IgorC [24]

After x seconds, an object will fall $\frac{1}{2}at^2$ where a is acceleration due to gravity and t is time

so when t=3.3
the distance it will fall is $(\frac{1}{2})(9.8\frac{m}{s^2})(3.3m)^2$ =53.361m
it will fal 53.361 meters

6 0

3 years ago

a student in your class says "electromagnetic waves can travel through outer space but mechanical waves can’t.” is it this stude

Kitty [74]

Answer:

Right

Explanation:

electromagnetic waves can travel through space (a vacuum) because it doesn't need a medium and its particles to propagate whereas a mechanical wave needs a medium to propagate. For example sound is a mechanical wave, sound vibrates off a mediums particles to propagate and for sound to be heard and travel

7 0

2 years ago

A circus acrobat is shot out of a cannon with an initial upward speed of 34 ft/s. if the acrobat leaves the cannon 4 ft above th

jok3333 [9.3K]

<h2>It will take 0.125 seconds to reach the net.</h2>

Explanation:

Initial speed, u = 34 ft/s = 10.36 m/s

Acceleration, a = -9.81 m/s²

Displacement, s = Final height - Initial height = 8 - 4 = 4 ft = 1.22 m

We have equation of motion, s = ut + 0.5 at²

Substituting

s = ut + 0.5 at²

1.22 = 10.36 x t + 0.5 x -9.81 x t²

4.905t² - 10.36 t + 1.22 = 0

t = 1.99 s or t = 0.125 seconds

Minimum time is 0.125 seconds.

It will take 0.125 seconds to reach the net.

6 0

3 years ago

__________ is when a person becomes less sensitive to a drug. A. Tolerance B. Craving C. Addiction D. Dependence

Luden [163]

A) Tolerance

Tolerance is developed after using a drug repeatedly, so the body adapts to it. Because of that, people who develop a tolerance would then need to use more of that drug to get the same effect.

4 0

3 years ago