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
torisob [31]
2 years ago
12

A 97.3 kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.67 r

ad/s . A monkey drops a 9.67 kg bunch of bananas vertically onto the platform. They hit the platform at 45 of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 21.9 kg , drops vertically to the edge of the platform, grasps it, and continues to rotate with the platform. Find the angular velocity of the platform with its load. Model the platform as a disk of radius 1.73 m
Physics
1 answer:
Yuliya22 [10]2 years ago
5 0

Answer:

w = 1.14 rad / s

Explanation:

This is an angular momentum exercise. Let's define a system formed by the three bodies, the platform, the bananas and the monkey, in such a way that the torques during the collision have been internal and the angular momentum is preserved.

Initial instant. The platform alone

        L₀ = I w₀

Final moment. When the bananas are on the shelf

we approximate the bananas as a point load and the distance is indicated

x = 0.45m

        L_f = (m x² + I ) w₁

angular momentum is conserved

         L₀ = L_f

         I w₀ = (m x² + I) w₁

         w₁ = \frac{I}{m x^2 + I}  \ w_o

Let's repeat for the platform with the bananas and the monkey is the one that falls for x₂ = 1.73 m

initial instant. The platform and bananas alone

        L₀ = I₁ w₁

         I₁ = (m x² + I)

           

final instant. After the crash

        L_f = I w

        L_f = (I₁ + M x₂²) w

the moment is preserved

        L₀ = L_f

        (m x² + I) w₁ = ((m x² + I) + M x₂²) w

         (m x² + I) w₁ = (I + m x² + M x₂²) w

we substitute

         w =  \frac{m x^2 +I}{I + m x^2 + M x_2^2} \ \frac{I}{m x^2 + I} \ w_o

         w =  \frac{I}{I + m x^2 + M x_2^2} \ w_o

the moment of inertia of a circular disk is

         I = ½ m_p x₂²

we substitute

         w =  \frac{ \frac{1}{2} m_p x_2^2 }{ \frac{1}{2} m_p x_2^2 + M x_2^2 + m x^2} \ \ w_o

let's calculate

          w =\frac{ \frac{1}{2} \ 97.3 \ 1.73^2 }{ \frac{1}{2} \ 97.3 \ 1.73^2 + 21.9 \ 1.73^2 + 9.67 \ 0.45^2 } \ \ 1.67

          w =  \frac{145.60 }{145.60 \ + 65.54 \ + 1.958} \ \ 1.67

          w = 1.14 rad / s

You might be interested in
NEED THE ANSWER PLZ<br><br>What are lanthanides?
geniusboy [140]
It is the the ecrins of light
5 0
3 years ago
Forces that are equal in size but opposite in direction are called what ?
enot [183]

Answer:

I think they are called balanced forces

Explanation:

3 0
2 years ago
Read 2 more answers
2. A company hires a security firm to patrol their stores and watch out for thieves. What is this an example of?
Lunna [17]

Answer:

someone hiring someone

Explanation:

4 0
3 years ago
Find the average speed of a walk to school and back if you took 12 minutes to walk there and 18 minutes to get back
nikdorinn [45]

Answer:

12+ 18 divide by 2 is the average minutes

7 0
2 years ago
Convert 5.5 kilometers into millimeters.​
dimaraw [331]

Answer:

5500000 millimeters

Explanation:

1 kilometre= 1000 meter

5.5 km=5.5 * 1000

=5500

Now,

1 metre = 1000 millimetres

5500 metre=1000*5500

=5500000 mm

4 0
1 year ago
Other questions:
  • 2. While standing near a bus stop, a student hears a distant horn beeping. The frequency emitted by the horn is 440 Hz. The bus
    5·1 answer
  • Suppose you go outside and look at three stars. Star A is blue, star B is white, and star C is red. Which star is the hottest, a
    5·2 answers
  • At a race track, a car of mass 1150 kg crashes into a concrete wall at a speed of 85 m/s a. If the car comes to a stop when it h
    10·1 answer
  • How is a pareto chart different from a standard vertical bar​ graph?
    12·1 answer
  • Frequency is the ____________ that move past a point during a specific amount of time. Frequency is measured in ____________ , a
    15·1 answer
  • I need help with this problem​
    8·1 answer
  • A student using a tuning fork of frequency 512 Hz observes that the speed of sound is 340.0 m/s. What is the wavelength of this
    6·1 answer
  • Which of the following has the same unit as the moment of force?
    8·2 answers
  • The sun shines equally on both hemispheres during the summer and winter solstices.
    10·1 answer
  • Two people stand facing each other at a roller skating rink then push off each other. a). What is the momentum of the system bef
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!