Ask question

Ask question

All categories

2 years ago

9

A top is a toy that is made to spin on its pointed end by pulling on a string wrapped around the body of the top. The string has

a length of 51 cm and is wrapped around the top at a place where its radius is 1.8 cm. The thickness of the string is negligible. The top is initially at rest. Someone pulls the free end of the string, thereby unwinding it and giving the top an angular acceleration of 10 rad/s2. What is the final angular velocity of the top when the string is completely unwound

1 answer:

AlladinOne [14]2 years ago

3 0

Given Information:

Angular displacement = θ = 51 cm = 0.51 m

Radius = 1.8 cm = 0.018 m

Initial angular velocity = ω₁ = 0 m/s

Angular acceleration = α = 10 rad/s ²

Required Information:

Final angular velocity = ω₂ = ?

Answer:

Final angular velocity = ω₂ = 21.6 rad/s

Explanation:

We know from the equations of kinematics,

ω₂² = ω₁² + 2αθ

Where ω₁ is the initial angular velocity that is zero since the toy was initially at rest, α is angular acceleration and θ is angular displacement.

ω₂² = (0)² + 2αθ

ω₂² = 2αθ

ω₂ = √(2αθ)

We know that the relation between angular displacement and arc length is given by

s = rθ

θ = s/r

θ = 0.51/0.018

θ = 23.33 radians

finally, final angular velocity is

ω₂ = √(2αθ)

ω₂ = √(2*10*23.33)

ω₂ = 21.6 rad/s

Therefore, the top will be rotating at 21.6 rad/s when the string is completely unwound.

You might be interested in

An electron has a kinetic energy of 3.00 ev. find its wavelength. (b) what if? a photon has energy 3.00 ev. find its wavelength.

Harman [31]

(a) The electron kinetic energy is
$K=3.00 eV$
which can be converted into Joule by keeping in mind that
$1 eV=1.6 \cdot 10^{-19}eV$
So that we find
$K=3.00 eV \cdot 1.6 \cdot 10^{-19} eV/J =4.8 \cdot 10^{-19}J$

The kinetic energy of the electron is related to its momentum p by:
$K= \frac{p^2}{2m}$
where m is the electron mass. Re-arranging the equation, we find
$p= \sqrt{ 2Km}= \sqrt{ 2 ( 4.8 \cdot 10^{-19} J)(9.1 \cdot 10^{-31} kg) } =9.35 \cdot 10^{-25} kgm/s$

And now we can use De Broglie's relationship to find its wavelength:
$\lambda= \frac{h}{p}= \frac{6.6 \cdot 10^{-34} Js}{9.35 \cdot 10^{-25} kg m/s} =7.06 \cdot 10^{-10}m$
where h is the Planck constant.

(b) By using the same procedure of part (a), we can convert the photon energy into Joules:
$E=3.00 eV \cdot 1.6 \cdot 10^{-19} eV/J =4.8 \cdot 10^{-19}J$

The energy of a photon is related to its frequency f by:
$E=hf$
where h is the Planck constant. Re-arranging the equation, we find
$f= \frac{E}{h}= \frac{4.8 \cdot 10^{-19} J}{6.6 \cdot 10^{-34}Js} =7.27 \cdot 10^{14}Hz$

And now we can use the relationship between frequency f, speed of light c and wavelength $\lambda$ of a photon, to find its wavelength:
$\lambda= \frac{c}{f}= \frac{3 \cdot 10^8 m/s}{7.27 \cdot 10^{14} Hz} =4.13 \cdot 10^{-7} m$

8 0

3 years ago

Which of these is a substance or compound that kills or inhibits bacteria?

saveliy_v [14]

Answer:

an antibiotic

Explanation:

4 0

2 years ago

Work is done on an object when an applied force causes the object to move in the same direction as the force.

Lelu [443]

Answer:yes

Explanation:

Work is done on an object when an applied force causes the object to move in the same direction as the force

3 0

3 years ago

If a sample of a radioactive isotope has a half-life of 1 year, how much of the original sample will be left at the end of the s

Tasya [4]

Answer:

1/4 of the original

Explanation:

That would be TWO half lives:

1/2 * 1/2 = 1/4 <======= 1/4 would be left

4 0

3 months ago

4. What is the acceleration of a rock if the net

HACTEHA [7]

Answer:

0.75 m/s²

Explanation:

Newton's second law:

∑F = ma

3 N = (4 kg) a

a = 0.75 m/s²

8 0

3 years ago