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
Agata [3.3K]
3 years ago
11

An Atwood machine consists of a mass of 3.5 kg connected by a light string to a mass of 6.0 kg over a frictionless pulley with a

moment of inertia of 0.0352 kg m2 and a radius of 12.5 cm. If the system is released from rest, what is the speed of the masses after they have moved through 1.25 m if the string does not slip on the pulley?
Please note: the professor has told us that the correct answer is 2.3 m/s. how does one arrive at this answer?
Physics
1 answer:
Andreas93 [3]3 years ago
8 0

Answer:

v=2.28m/s

Explanation:

For the first mass we have m_1=3.5kg, and for the second m_2=6.0kg. The pulley has a moment of intertia I_p=0.0352kgm^2 and a radius r_p=0.125m.

We solve this with conservation of energy.  The initial and final states in this case, where no mechanical energy is lost, must comply that:

K_i+U_i=K_f+U_f

Where K is the kinetic energy and U the gravitational potential energy.

We can write this as:

K_f+U_f-(K_i+U_i)=(K_f-K_i)+(U_f-U_i)=0J

Initially we depart from rest so K_i=0J, while in the final state we will have both masses moving at velocity <em>v</em> and the tangential velocity of the pully will be also <em>v</em> since it's all connected by the string, so we have:

K_f=\frac{m_1v^2}{2}+\frac{m_2v^2}{2}+\frac{I_p\omega_p^2}{2}=(m_1+m_2+\frac{I_p}{r_p^2})\frac{v^2}{2}

where we have used the rotational kinetic energy formula and that v=r\omega

For the gravitational potential energy part we will have:

U_f-U_i=m_1gh_{1f}+m_2gh_{2f}-(m_1gh_{1i}+m_2gh_{2i})=m_1g(h_{1f}-h_{1i})+m_2g(h_{2f}-h_{2i})

We don't know the final and initial heights of the masses, but since the heavier, m_2, will go down and the lighter, m_1, up, both by the same magnitude <em>h=1.25m </em>(since they are connected) we know that h_{1f}-h_{1i}=h and h_{2f}-h_{2i}=-h, so we can write:

U_f-U_i=m_1gh-m_2gh=gh(m_1-m_2)

Putting all together we have:

(K_f-K_i)+(U_f-U_i)=(m_1+m_2+\frac{I_p}{r_p^2})\frac{v^2}{2}+gh(m_1-m_2)=0J

Which means:

v=\sqrt{\frac{2gh(m_2-m_1)}{m_1+m_2+\frac{I_p}{r_p^2}}}=\sqrt{\frac{2(9.8m/s^2)(1.25m)(6.0kg-3.5kg)}{3.5kg+6.0kg+\frac{0.0352kgm^2}{(0.125m)^2}}}=2.28m/s

You might be interested in
A basketball is filled with air and has a small hole. Explain why the basketball would leak.
Assoli18 [71]
Because it has a small hole and air is like water, an area of higher pressure wants to move to a lower pressure area.
4 0
3 years ago
Read 2 more answers
If cake baking is compared to protein synthesis, what genetic structure would be analogous to the flour, sugar, and eggs?
galina1969 [7]
Mrnmrnamrnamrnamrnamrnamrnamrnamrnamrnamrna
7 0
3 years ago
What question was asked by Faraday that the narrator calls a leap
masha68 [24]
<span> If electricity and magnetism can create motion, can the reverse be true? Can motion and magnetism create electricity?</span>
4 0
3 years ago
Read 2 more answers
A substance that does not react with metal, has a bitter taste, and turns litmus paper blue is a(n) ___.
Pavlova-9 [17]
The answer to the question is b because acid is a substance that tastes sour, reacts with metal and turns litmus paper blue
5 0
3 years ago
A boat moves with a speed of +2.5 m/s in a direction 25° north of east. If the mass of the boat is 15,000 kg, what is the moment
nadya68 [22]
Momentum - mass in motion
P=MV
P=(15,000 kg)(2.5 m/s)
P=37 500 kg x m/s to the north
Hope this helps
5 0
3 years ago
Other questions:
  • What is the advantage of D-step tuning on 2020 Pathfinder’s Xtronic CVT at cruising speed?
    10·1 answer
  • A ball thrown vertically upward is caught by the thrower after 1.76 s. find the initial velocity of the ball. the acceleration o
    9·1 answer
  • Sort the chemical equations based on the chemical reactions they represent.
    13·2 answers
  • What is the power p supplied to a resistor whose resistance is r when it is known that it has a voltage δv across it?
    13·1 answer
  • A dwarf planet discovered out beyond the orbit of Pluto is known to have an orbital period of 619.36 years. What is its average
    13·1 answer
  • What are the advantages of parallel circuits? Check all that apply
    11·2 answers
  • What 3 factors should be considered when designing a lighting rod?
    10·1 answer
  • Can it is possible to complete half syllabus of physics class 11 in 8 days?​
    13·1 answer
  • A small airplane is sitting at rest on the ground. Its center of gravity is 2.58 mm behind the nose of the airplane, the front w
    12·1 answer
  • For an object on a flat surface, the force of gravity is 10 newtons downward and the normal force is 10 newtons upward. The appl
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!