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
tresset_1 [31]
3 years ago
5

A physics student of mass 43.0 kg is standing at the edge of the flat roof of a building, 12.0 m above the sidewalk. An unfriend

ly dog is running across the roof toward her. Next to her is a large wheel mounted on a horizontal axle at its center. The wheel, used to lift objects from the ground to the roof, has a light crank attached to it and a light rope wrapped around it; the free end of the rope hangs over the edge of the roof. The student radius 0.300 m and a moment of inertia of 9.60 kg m^2 for rotation about the axle, how long does it take her to reach the side walk, and how fast will she be moving just beofre she lands?
Physics
1 answer:
Dmitry_Shevchenko [17]3 years ago
5 0

Answer:

The speed of the student just before she lands, v₂ is approximately 8.225 m/s

Explanation:

The given parameters are;

The mass of the physic student, m = 43.0 kg

The height at which the student is standing, h = 12.0 m

The radius of the wheel, r = 0.300 m

The moment of inertia of the wheel, I = 9.60 kg·m²

The initial potential energy of the female student, P.E.₁ = m·g·h₁

Where;

m = 43.0 kg

g = The acceleration due to gravity ≈ 9.81 m/s²

h = 12.0 h

∴ P.E.₁ = 43 kg × 9.81 m/s² × 12.0 m = 5061.96 J

The kinetic rotational energy of the wheel and kinetic energy of the student supporting herself from the rope she grabs and steps off the roof, K₁, is given as follows;

K_1 = \dfrac{1}{2} \cdot m \cdot v_{1}^2+\dfrac{1}{2} \cdot I \cdot \omega_{1}^2

The initial kinetic energy, 1/2·m·v₁² and the initial kinetic rotational energy, 1/2·m·ω₁² are 0

∴ K₁ = 0 + 0 = 0

The final potential energy of the student when lands. P.E.₂ = m·g·h₂ = 0

Where;

h₂ = 0 m

The final kinetic energy, K₂, of the wheel and student is give as follows;

K_2 = \dfrac{1}{2} \cdot m \cdot v_{2}^2+\dfrac{1}{2} \cdot I \cdot \omega_{2}^2

Where;

v₂ = The speed of the student just before she lands

ω₂ = The angular velocity of the wheel just before she lands

By the conservation of energy, we have;

P.E.₁ + K₁ = P.E.₂ + K₂

∴ m·g·h₁ + \dfrac{1}{2} \cdot m \cdot v_{1}^2+\dfrac{1}{2} \cdot I \cdot \omega_{1}^2 = m·g·h₂ + \dfrac{1}{2} \cdot m \cdot v_{2}^2+\dfrac{1}{2} \cdot I \cdot \omega_{2}^2

Where;

ω₂ = v₂/r

∴ 5061.96 J + 0 = 0 + \dfrac{1}{2} \times 43.0 \, kg \times v_{2}^2+\dfrac{1}{2} \times 9.60 \, kg\cdot m^2 \cdot \left (\dfrac{v_2}{0.300 \, m} }\right ) ^2

5,061.96 J = 21.5 kg × v₂² + 53.\overline 3 kg × v₂² = 21.5 kg × v₂² + 160/3 kg × v₂²

v₂² = 5,061.96 J/(21.5 kg + 160/3 kg) ≈ 67.643118 m²/s²

v₂ ≈ √(67.643118 m²/s²) ≈ 8.22454363 m/s

The speed of the student just before she lands, v₂ ≈ 8.225 m/s.

You might be interested in
Which method of separation would work on a homogeneous mixture salt water
Butoxors [25]
To separate a mixture of salt and water, you can try first by using filter paper hen with the extra water part set it out to the window so that the salt water evaporates and only the salt is remaining.
5 0
3 years ago
Read 2 more answers
A 50 W light bulb is plugged into a standard
wolverine [178]

Answer:

$1.26

Explanation:

Power =energy/ time

energy =powerxtime

energy =50x31x24=37200

=37.2kwh

1kwh =3.39

37.2kwh=3.39x37.2=126.108cent

=$1.26

8 0
2 years ago
(3.16_Q2) Which weights would you use on a single thread to create a 6.86 N force? Question 2 options: Weight IDs A, B, C, D Wei
Tomtit [17]

1. E,F

2. D,E,F

3. B,C,E,G

4. A,B,C,D

I did the test! :)

5 0
3 years ago
Describe the difference between balanced forces and action/reaction forces
Alecsey [184]
 Balanced forces<span> act on the same object and </span>Action-Reaction forces<span> act on different objects.</span>
5 0
3 years ago
Read 2 more answers
Which of the following accurately describes the behavior of water when subject to temperature change? A. The volume of water wil
nata0808 [166]

Choices 'C' and 'D' are both correct.

(Except in 'C', changing the temperature from 1°C to 3°C is not usually
described as 'cooling', and it's not the water's 'mass' that changes.  But
water does contract in volume during that change.)
8 0
3 years ago
Other questions:
  • Three different planet-star systems, which are far apart from one another, are shown above. The masses of the planets are much l
    15·1 answer
  • 1. Si tengo medio kilo de fruta y te doy un cuarto y tú me das tres cuartos de kilo, ¿cuánto tengo? 2. Si en una carrera te qued
    13·1 answer
  • Planet z has a rocky surface. at height 3240 km above the surface, the gravitational acceleration is what is the radius of the p
    13·1 answer
  • Calculate the force of gravity on the 1.2-kg mass if it were 1.9×107 m above earth's surface (that is, if it were four earth rad
    9·1 answer
  • How many electrons make up a charge of 3.5kC?
    9·2 answers
  • Why cant you feel the force attraction between mars
    11·1 answer
  • A water dwelling slug like animal
    14·2 answers
  • If the radius of Earth were one half what it is now, and the mass were the same, what would be the value of g?
    15·2 answers
  • HELLPPP WILL GIVE B IF CORRECT NEED IT FAST!!!! Please help me
    6·1 answer
  • Draw the Free- Body diagram of the 37 kilogram glass falling to the floor in a vacuum.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!