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DaniilM [7]
3 years ago
9

A simple pendulum, consisting of a mass on a string of length L, is undergoing small oscillations with amplitude A.

Physics
1 answer:
Leya [2.2K]3 years ago
4 0

Answer:

A. Period is halved

Explanation:

The period of a pendulum swing, T, is given in terms of mass as:

T = 2\pi \sqrt{\frac{I}{mgL} }

where I = moment of inertia

m = mass of the pendulum

g = acceleration due to gravity

h = Length of string

If the mass is increased by a factor of 4, that means:

M = 4m

(M = new mass)

The new period of the pendulum, T_n, will now be:

T_n = 2\pi \sqrt{\frac{I}{MgL} }\\\\\\T_n = 2\pi \sqrt{\frac{I}{4mgL} }\\\\\\T_n = 2\pi \sqrt{\frac{1}{4} * \frac{I}{mgL} }\\\\\\T_n = \frac{2\pi}{2}  \sqrt{\frac{I}{mgL} }\\\\\\T_n = \frac{1}{2} * 2\pi \sqrt{\frac{I}{mgL} }\\\\\\T_n = \frac{1}{2} * T

Hence, the period is halved.

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A yo‑yo with a mass of 0.0800 kg and a rolling radius of =2.70 cm rolls down a string with a linear acceleration of 5.70 m/s2.
N76 [4]

Explanation:

Given that,

Mass, m = 0.08 kg

Radius of the path, r = 2.7 cm = 0.027 m

The linear acceleration of a yo-yo, a = 5.7 m/s²

We need to find the tension magnitude in the string and the angular acceleration magnitude of the yo‑yo.

(a) Tension :

The net force acting on the string is :

ma=mg-T

T=m(g-a)

Putting all the values,

T = 0.08(9.8-5.7)

= 0.328 N

(b) Angular acceleration,

The relation between the angular and linear acceleration is given by :

\alpha =\dfrac{a}{r}\\\\\alpha =\dfrac{5.7}{0.027}\\\\=211.12\ m/s^2

(c) Moment of inertia :

The net torque acting on it is, \tau=I\alpha, I is the moment of inertia

Also, \tau=Fr

So,

I\alpha =Fr\\\\I=\dfrac{Fr}{\alpha }\\\\I=\dfrac{0.328\times 0.027}{211.12}\\\\=4.19\times 10^{-5}\ kg-m^2

Hence, this is the required solution.

3 0
3 years ago
What is Acceleration?​
earnstyle [38]

Acceleration is the rate of change of velocity

 

To define acceleration, We need to know more about motion.

Motion: This can be defined as the change in position of a body from one point to another. When an object accelerates, it undergoes motion.

<u>Definition</u>

Acceleration can be defined as the rate of change of velocity. The S.I unit of acceleration is meter-per-squared seconds. (m/s²)

The formula of acceleration is

  • a = (v-u)/t................. Equation 1

⇒ Where:

  • a = acceleration
  • u = initial velocity
  • v = final velocity
  • t = time

Hence, Acceleration is the rate of change of velocity

Learn more about acceleration here: brainly.com/question/605631

5 0
2 years ago
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In this system, the equilibrium lies to the<br> and the reaction favors the
vfiekz [6]

Answer: reactants to this system,...

Explanation:

7 0
3 years ago
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A uniform ladder 5.0 m long rests against a frictionless, vertical wall with its lower end 3.0 m from the wall. The ladder weigh
dem82 [27]

Answer:

Explanation:

a )

Reaction force of the ground

R = mg

= 160 N

Maximum friction force possible

= μ x R

= μ x 160

= .4 x 160

= 64 N .

b )

 160 N will act at middle point . 740N will act at distance of 3 / 5 m from the wall ,

Taking moment about top point of ladder

160 x 1.5 + 740 x 3/5 + f x 4 = 900 x 3

240 + 444 + 4f = 2700

f = 504 N

c )

Let x be the required distance.  

Taking moment about top point of ladder

160 x 1.5 + 740 x 3 x / 5 + .4 x 900 x 4  = 900 x 3  ( .4 x 900 is the maximum friction possible )

240 + 444 x + 1440  = 2700

x = 2.3  m

so man can go upto 2.3 at which maximum friction acts .

8 0
3 years ago
4. Uncle Harry weighs 180 pounds. What is his mass in kilograms?
MatroZZZ [7]
180 pounds (lb) converts to 81.647 kilograms (kg).
5 0
3 years ago
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