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
Which factors would increase heating of Earth, and which factors would decrease it
loris [4]

Answer:

So as sunlight continued to enter the box and the walls continued to warm, heat built up inside and increased the temperature.

4 0
3 years ago
Read 2 more answers
An inclined plane creates a mechanical advantage of 5. What would the input force need to be to create an output force of 20 N?
nlexa [21]
A) 15 N
Don’t click the link it will give you viruses!
4 0
2 years ago
a family drives from boston (100 miles away) to new york (500 miles away) in 10 hours . How fast were they were traveling?
Fynjy0 [20]

It should be 60 mph. Because if  you divide 600 by 10 it’s 60

8 0
3 years ago
An ideal gas is enclosed in a piston, and 1600 J of work is done on the gas. As this happens, the internal energy of the gas inc
Phantasy [73]

Answer:

- 1100 J heat flows out

Explanation:

dW = - 1600 J (as work is done on the gas)

dU = 500 J

dQ = ?

According to the first law of thermodynamics

dQ = dU + dW

dQ = 500 - 1600

dQ = - 1100 J

As heat is negative so it flows out.

3 0
3 years ago
Define density<br><br> Please help!!
Romashka-Z-Leto [24]

, density is how compact an object is. Put another way, density is the mass of an object divided by its volume.

5 0
3 years ago
Other questions:
  • Which two biomes have little precipitation?
    8·1 answer
  • Energy is conventionally measured in Calories as well as in joules. One Calorie in nutrition is one kilocalorie, defined as 1 kc
    11·1 answer
  • A scientist wants to calculate the kinetic energy of a cheetah as it chases down its prey. What does the scientist need to measu
    5·2 answers
  • Is a cookie crumbling or in other words breaking a cookie a physical change?
    13·2 answers
  • An atom has 1.5x10^19 free electrons.
    12·1 answer
  • A cube of wood 15.0 cm on each side is tied to the bottom of a tank filled with water to a depth of 50 cm. The tension in the st
    14·1 answer
  • A lorry pulls forward after initially being stationary, it takes the lorry 80m to reach a speed of
    12·1 answer
  • What would happen if the Earth stopped rotating?
    15·1 answer
  • The door handles are kept near the door handles​
    7·1 answer
  • The two forces to the right are friction which one would be the force of kinetic friction?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!