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4 years ago

For small angles, does the pendulum's period of oscillation depend on initial angular displacement from equilibrium? Explain.

Physics

1 answer:

aksik [14]4 years ago

6 0

Answer:

No, the pendulum's period of oscillation does not depend on initial angular displacement.

Explanation:

Given that,

For small angle, the pendulum's period of oscillation depend on initial angular displacement from equilibrium.

We know that,

The time period of pendulum is defined as

$T=2\pi\sqrt{\dfrac{l}{g}}$

Where, l = length of pendulum

g = acceleration due to gravity

So, The time period of pendulum depends on the length of pendulum and acceleration due to gravity.

It does not depend on the initial angular displacement.

Hence, No, the pendulum's period of oscillation does not depend on initial angular displacement.

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A basketball player jumps straight up for a ball. To do this, he lowers his body 0.310 m and then accelerates through this dista

Nastasia [14]

Answer:A)u =4.295m/s , B)a = 29.746m/s² C) F=3,153N

Explanation:

Using the kinematic expression

v² = u² - 2as

where

u = initial velocity

v = final velocity

s = distance

g = acceleration due to gravity .

Given that he reaches a height of 0.940 m above the floor,

the final velocity = 0

Here, acceleration due to gravity is acting in opposite the initial direction of motion. So, a=-9.81 m/s.

v² = u² + 2as

0² - u² = 2 (- 9.81) × 0.940

- u² = 2 × - 9.81 × 0.920

- u² = -18.4428

cancelling the minus in both sides , we have that

u² = 18.4428

u = √18.4428

u =4.295m/s

(b) His acceleration (in m/s2) while he is straightening his legs. He goes from zero to the velocity found in part (a) in a distance of 0.310 m. m/s2

Using v² = u² + 2as

where u = initial speed of basketball player before lengthening = 0 m/s,

v = final speed of basketball player after lengthening = 4.295m/s,

a = acceleration while straightening his legs

s = distance moved during lengthening = 0.310m

v² = u² + 2as

a = (v² - u²)/2s

a = (4.29m/s)² - (0 m/s)²)/(2 × 0.310m)

a = (18.4428 m²/s² - 0 m²/s²)/(0.62 m)

a = (18.4428 m²/s²/(0.62 m)

a = 29.746m/s²

c) The force (in N) he exerts on the floor to do this, given that his mass is 106 kg. N

Force= mass x acceleration.

F = 106 kg X 29.746m/s²

F = 3,153.076 rounded to 3,153N

8 0

3 years ago

Time running out plzz hurry!!!!!!

Vesnalui [34]

I think you would hear a lower pitch

3 0

3 years ago

Read 2 more answers

The spring in the muzzle of a child's spring gun has a spring constant of 730 N/m. To shoot a ball from the gun, first the sprin

Korolek [52]

Answer:

a. V=11.84 m/s

b.x=0.052m

Explanation:

a).

Given

$K=730 N/m$ , $m=0.053kg$ , $h=1.90m$ .

$v_f^2=v_i^2+2*g*h$

$v_i^2=2*g*h=2*9.8m/s^2*1.9m$

$v_i=\sqrt{2*9.8m/s^2*1.9m}=\sqrt{37.24 m^2/s^2}$

$v_i=6.1 m/s$

$v_i=V*sin(31)$

$V=\frac{v_i}{sin(31)}=\frac{6.1m/s}{sin(31)}$

$V=11.84 m/s$

b).

$K_k=\frac{1}{2}*K*x^2$

No friction on the ball so:

$x^2=\frac{2*K_k}{K}$

$x=\sqrt{\frac{2*0.053kg*9.8m/s^2*1.9m}{730N/m}}$

$x=\sqrt{2.7x10^{-3}m^2}=0.052m$

5 0

3 years ago

PLZ HELP

Nadya [2.5K]

1) The mass of the continent is $3.3\cdot 10^{21}kg$

2) The kinetic energy of the continent is 1683 J

3) The speed of the jogger must be 6.57 m/s

Explanation:

The continent can be represented as a slab of size

$d=5850 km = 5.85\cdot 10^6 m$

and depth

$t = 35 km = 3.5\cdot 10^4 m$

So its volume is

$V=d^2 t = (5.85\cdot 10^6)^2(3.5\cdot 10^4)=1.20\cdot 10^{18} m^3$

We also know that the density of the continent is

$\rho = 2750 kg/m^3$

Therefore, we can calculate its mass as:

$m=\rho V=(2750)(1.20\cdot 10^{18})=3.3\cdot 10^{21} kg$

The kinetic energy of the continent is given by

$K=\frac{1}{2}mv^2$

where

m is its mass

v is its speed

We have already calculate its mass, while the speed is

v = 3.2 cm/year

We have to convert into SI units first, as follows:

$v=3.2 \frac{cm}{year} \cdot \frac{1}{100 cm/m} \cdot \frac{1}{(365 d/y)(24h/d)(60min/h)(60 s/min)}=1.01\cdot 10^{-9} m/s$

The mass is

$m=3.3\cdot 10^{21} kg$

So, the kinetic energy of the continent is

$K=\frac{1}{2}(3.3\cdot 10^{21})(1.01\cdot 10^{-9})^2=1683 J$

Here we have a jogger having the same kinetic energy of the continent, so

$K=1683 J$

And the kinetic energy of the jogger can be expressed as

$K=\frac{1}{2}mv^2$

where

m = 78 kg is the mass of the jogger

v is his speed

We can therefore re-arrange the equation to find the speed of the man, and we get:

$v=\sqrt{\frac{2K}{m}}=\sqrt{\frac{2(1683)}{78}}=6.57 m/s$

Learn more about kinetic energy:

brainly.com/question/6536722

#LearnwithBrainly

8 0

3 years ago

What do you think is the main idea?

Tanzania [10]

I think the main idea is that the middle planets have a solid inner core and that they all could have life on them

3 0

3 years ago