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
Snowcat [4.5K]
3 years ago
12

A stick is resting on a concrete step with 2/5 of its length hanging over the edge. A single ladybug lands on the end of the sti

ck hanging over the edge, and the stick begins to tip. A moment later, a second, identical ladybug lands on the other end of the stick, which results in the stick coming momentarily to rest 41.3° from the horizontal. If the mass of each bug is 3.43 times the mass of the stick and the stick is 18.7 cm long, what is the magnitude of the angular acceleration of the stick at the instant?
Physics
1 answer:
Trava [24]3 years ago
3 0
The moment the stick comes to rest at θ=62.1° from horizontal. 

<span>Angular acceleration = (net torque) / (moment of inertia) </span>
<span>α = τ/I </span>

<span>We have to add up the torques due to the bugs and the stick; and add up the moments of inertia due to all three also. </span>

<span>Let L be the stick's length and let m be the stick's mass (so "2.75m" is each bug's mass). And let's say the "lower" ladybug is on the left. Then the lower ladybug exerts this much torque: </span>

<span>τ_lowerbug = −(2/5)L(2.75mg)cosθ (negative because I am (arbitrarily) choosing counter-clockwise as the negative angular direction). </span>

<span>The upper ladybug exerts this much torque: </span>

<span>τ_upperbug = +(3/5)L(2.75mg)cosθ </span>

<span>The weight of the stick can be assumed to act through its center, which is 1/10 of the way from the fulcrum. So the stick exerts this much torque: </span>

<span>τ_stick = +(1/10)L(mg)cosθ </span>

<span>The net torque is thus: </span>

<span>τ_net = τ_lowerbug + τ_upperbug + τ_stick </span>
<span>= −(2/5)L(2.75mg)cosθ + (3/5)L(2.75mg)cosθ + (1/10)L(mg)cosθ </span>
<span>= (2.75(3/5−2/5)+1/10)(mgL)cosθ </span>

<span>Now for the moments of inertia. The bugs can be considered point masses of "2.75m" each. So for each of them you can use the simple formula: I=mass×R²: </span>

<span>I_lowerbug = (2.75m)((2/5)L)² = (2.75m)(4/25)L² </span>
<span>I_upperbug = (2.75m)((3/5)L)² = (2.75m)(9/25)L² </span>

<span>For the stick, we can use the parallel axis theorem. This says, when rotating something about an axis offset a distance "R" from its center of mass, the moment of inertia is: </span>

<span>I = I_cm + mR² </span>

<span>We know that for a stick about its center of mass, I_cm is (1/12)mL² (see many sources). And in this problem we know that it's offset by R=(1/10)L. So: </span>

<span>I_stick = (1/12)mL² + m((1/10)L)² </span>
<span>= (1/12)mL² + (1/100)mL² </span>
<span>= (7/75)mL² </span>

<span>So the total moment of inertia is: </span>

<span>I_total = I_lowerbug + I_upperbug + I_stick </span>
<span>= (2.75m)(4/25)L² + (2.75m)(9/25)L² + (7/75)mL² </span>
<span>= (2.75(4/25+9/25)+7/75)mL² </span>

<span>So that means the angular acceleration is: </span>

<span>α = τ_net/I_total </span>
<span>= ((2.75(3/5−2/5)+1/10)(mgL)cosθ)/((2.75(4... </span>

<span>The "m" cancels out. You're given "L" and "θ" and you know "g", so do the math (and don't forget to use consistent units).</span>
You might be interested in
What is the first law of thermodynamics?​
jok3333 [9.3K]

Answer:

it states that energy can neither be created or destroyed

4 0
2 years ago
Read 2 more answers
Two Earth satellites, A and B, each of mass m, are to be launched into circular orbits about Earth’s center. Satellite A is to o
Vera_Pavlovna [14]

Answer:

Explanation:

Orbital radius of satellite A , Ra = 6370 + 6370 = 12740 km

Orbital radius of satellite B , Rb = 6370 + 19110 = 25480 km

Orbital potential energy of a satellite = - GMm / r where G is gravitational constant , M is mass of the earth and m is mass of the satellite

Orbital potential energy of a satellite A = - GMm / Ra

Orbital potential energy of a satellite B = - GMm / Rb

PE of satellite B /PE of satellite A

=  Ra / Rb

= 12740 / 25480

= 1 / 2

b ) Kinetic energy of a satellite is half the potential energy with positive value , so ratio of their kinetic energy will also be same

KE of satellite B /KE of satellite A

= 1 / 2

c ) Total energy will be as follows

Total energy = - PE + KE

- P E + PE/2

= - PE /2

Total energy of satellite B / Total energy of A

= 1 / 2

Satellite B will have greater total energy because its negative value is less.

5 0
3 years ago
What technique is used by scientists to determine which of several explanations is the best explanation
jok3333 [9.3K]

Answer:

When conducting research, scientists use the scientific method to collect measurable, empirical evidence in an experiment related to a hypothesis (often in the form of an if/then statement), the results aiming to support or contradict a theory.

I HOPE ITS RIGHT

4 0
3 years ago
M = 30.3kg<br>M = 40.17kg 9<br>R = 0.5m<br>G = 6. 67x10^11<br>F ?​
Lena [83]

Answer:

m¹=30.3kg

m²=40.17kg

R=0.5m

G=6.67*10¹¹

F=Gm¹m²/R²

=160.68

4 0
3 years ago
Starting at t = 0 s , a horizontal net force F⃗ =( 0.285 N/s )ti^+(-0.460 N/s2 )t2j^ is applied to a box that has an initial mom
Irina-Kira [14]

Answer:

Explanation:

We know that Impulse = force x time

impulse = change in momentum

change in momentum = force x time

Force F = .285 t -.46t²

Since force is variable

change in momentum = ∫ F dt  where F is force

= ∫ .285ti - .46t²j dt

= .285 t² / 2i - .46 t³ / 3 j

When t = 1.9

change in momentum = .285 x 1.9² /2 i  -  .46 x 1.9³ / 3 j

= .514i - 1.05 j

final momentum

= - 3.1 i + 3.9j +.514i - 1.05j

= - 2.586 i + 2.85j

x component = - 2.586

y component = 2.85

7 0
3 years ago
Other questions:
  • Does a 2000 mercury cougar have a timing belt
    15·1 answer
  • A spaceship enters the solar system moving toward the Sun at a constant speed relative to the Sun. By its own clock, the time el
    9·1 answer
  • During a care on level ground, Andra runs with an average velocity of 6.02 m/s to the East. What distance does Andra cover in 13
    12·1 answer
  • Kamala puts on inline skates and stands facing a wall. When she pushes against the wall, she rolls backward. Why does pushing ha
    5·2 answers
  • A child of mass 47 kg sits on the edge of a merry-go-round with radius 1.3 m and moment of inertia 56.3953 kg m2 . The merrygo-r
    15·1 answer
  • A large truck breaks down out on the road and receives a push back to town by a small compact car.
    5·1 answer
  • When a compass needle settles down in a magnetic field, _______. the needle aligns itself with the field, the south end of the c
    8·1 answer
  • What does the kinetic theory say about the motion of atoms
    6·1 answer
  • Read this excerpt from Through the Looking-Glass by Lewis Carroll.
    14·2 answers
  • If mass is measured in kg and acceleration is measured in m/s^2, what units would force be measured in? This unit is also know a
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!