1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
fredd [130]
2 years ago
10

A thin, uniform stick of mass M and length L is at rest on a flat, frictionless surface to which one end of it is pinned. A smal

l mass m traveling at speed v collides with and attaches to the stick at a distance 2L/3 away from the end through which it is pinned to the surface. (a) Find an expression for the moment of inertia of the stick mass object after the collision. (b) Find an expression for the final angular speed of the combined object
Physics
1 answer:
labwork [276]2 years ago
6 0

Answer:

a)  I = (\frac{M}{3} + \frac{4m}{9}) L²  ,   b)     w = (\frac{27 M}{18 m} + 2)⁻¹  Lv₀

Explanation:

a) The moment of inertia is a scalar that represents the inertia in circular motion, therefore it is an additive quantity.

The moment of inertia of a rod held at one end is

         I₁ = 1/3 M L²

The moment of inertia of the mass at y = L

        I₂ = m y²

 

The total inertia method

        I = I₁ + I₂

        I = \frac{1}{3} M L² + m (\frac{2}{3} L)²

        I = (\frac{M}{3} +\frac{4m}{9} ) L²

   

b) The conservation of angular momentum, where the system is formed by the masses and the bar, in such a way that all the forces during the collision are internal.    

Initial instant. Before the crash  

       L₀ = I₂ w₀  

angular and linear velocity are related  

       w₀ = y v₀  

      w₀ = \frac{2}{3}L v₀  

      L₀ = I₂ y v₀  

Final moment. After the crash  

      L_{f} = I w

 

how angular momentum is conserved  

      L₀ = L_{f}

      I₂ y v₀ = I w

substitute

      m (\frac{2L}{3})² (\frac{2L}{3} v₀ =  (\frac{M}{3} +\frac{4m}{9} ) L²  w

      \frac{6}{27}  m L³ v₀ = (\frac{M}{3} +\frac{4m}{9} ) L²  w

        \frac{6}{27}  m L v₀ = (\frac{M}{3} +\frac{4m}{9} )   w

        L v₀ = (\frac{27 M}{18 m} + 2)  w     

       w = (\frac{27 M}{18 m} + 2)⁻¹  Lv₀

 

You might be interested in
A point charge of 5.7 µc moves at 4.5 × 105 m/s in a magnetic field that has a field strength of 3.2 mt, as shown in the diagram
Sauron [17]

The magnitude of the force on the charge by the influence of the magnetic field will be 6.6*10^-3 N

<h3>What is magnetic force?</h3>

Magnetic force, attraction or repulsion that arises between electrically charged particles because of their motion.The magnitude of the magnetic force acting on the charge is given by:

\rm F=qvBsin\theta

where

The magnitude of the charge   q=5.7\ \mu C =5.7\times 10^{-6} \ C

The velocity of the charge        v=4.5\times 10^5\ \frac{m}{s}

The magnitude of the magnetic field   3.2\ mT=0.0032\ T

The angle between the directions of v and B  \theta =90^o-37^o=53^o

By substituting the values we will get:

F=(5.7\times 10^}-6})(4.5\times 10^5)(0.0032)(Sin53^o)

F=6.6\times 10^{-3}\ N

Hence the magnitude of the force on the charge by the influence of the magnetic field will be 6.6*10^-3 N

To know more about Magnetic force follow

brainly.com/question/14411049

3 0
2 years ago
The rms (root-mean-square) speed of a diatomic hydrogen molecule at 50∘C is 2000 m/s. Note that 1.0 mol of diatomic hydrogen at
denis-greek [22]

Answer:

A) d. (1/4)(2000m/s) = 500 m/s

B) c. 4000 J

C) f. None of the above (2149.24 m/s)

Explanation:

A)

The translational kinetic energy of a gas molecule is given as:

K.E = (3/2)KT

where,

K = Boltzman's Constant = 1.38 x 1^-23 J/K

T = Absolute Temperature

but,

K.E = (1/2) mv²

where,

v = root mean square velocity

m = mass of one mole of a gas

Comparing both equations:

(3/2)KT = (1/2) mv²

v = √(3KT)/m  _____ eqn (1)

<u>FOR HYDROGEN:</u>

v = √(3KT)/m = 2000 m/s  _____ eqn (2)

<u>FOR OXYGEN:</u>

velocity of oxygen = √(3KT)/(mass of oxygen)  

Here,

mass of 1 mole of oxygen = 16 m

velocity of oxygen = √(3KT)/(16 m)

velocity of oxygen = (1/4) √(3KT)/m

using eqn (2)

<u>velocity of oxygen = (1/4)(2000 m/s) = 500 m/s</u>

B)

K.E = (3/2)KT

Since, the temperature is constant for both gases and K is also a constant. Therefore, the K.E of both the gases will remain same.

K.E of Oxygen = K.E of Hydrogen

<u>K.E of Oxygen = 4000 J</u>

C)

using eqn (2)

At, T = 50°C = 323 k

v = √(3KT)/m = 2000 m/s

m = 3(1.38^-23 J/k)(323 k)/(2000 m/s)²

m = 3.343 x 10^-27 kg

So, now for this value of m and T = 100°C = 373 k

v = √(3)(1.38^-23 J/k)(373 k)/(3.343 x 10^-27 kg)

<u>v = 2149.24 m/s</u>

<u></u>

8 0
3 years ago
What Electromagnetic has a shorter wavelength
True [87]
The electromagnetic that has a shorter wavelength is ultraviolet (UV)
3 0
3 years ago
Read 2 more answers
Using the right amount of significant figures, calculate the answer to the following problem, 215.5+101.02555
cestrela7 [59]

Answer:

This is how I figured it out:

  1. 215.5 rounded to one significant figure is 200
  2. 101.02555 rounded to one significant figure is 100.
  3. 200 + 100 = 300.

Hope this helps!

Explanation:

7 0
3 years ago
Two auto technicians are discussing the stages of engine operation. Auto Technician A says during the intake stage of engine ope
pav-90 [236]

Neither technician is correct.

Please don't touch my car.

7 0
3 years ago
Other questions:
  • A spider of mass mm is swinging back and forth at the end of a strand of silk of length LL. During the spider's swing the strand
    12·1 answer
  • For a body falling freely from rest​ (disregarding air​ resistance), the distance the body falls varies directly as the square o
    8·2 answers
  • Petroleum contains _____ energy.<br> A. light<br> B. kinetic<br> C. chemical<br> D. mechanical
    8·2 answers
  • According to the kinetic molecular theory, the pressure of a gas in a container will increase if the
    14·1 answer
  • passengers on an airplane move from rest to 73 meters per second before the airplane takes off. if the airplane takes 100 second
    12·1 answer
  • Write down the principal of lever​
    14·1 answer
  • What is energy and types of energy<br>​
    6·2 answers
  • Can you answer this math homework? Please!
    12·1 answer
  • How does the composition of a comet compare with that of the Sun?.
    6·1 answer
  • Linear Velocity What is the linear velocity in cm&gt;min for any edge point of a 12-cm-diameter CD (compact disc) spinning at 10
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!