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
Microwaves have a higher frequency than radio waves, so why is it that they don't travel faster?
Lubov Fominskaja [6]

Answer: Energy requirement or consumption also increases as frequency goes higher. Hence, those low-frequency to mid-frequency waves are commonly referred to as radio waves and essentially, they have longer wavelengths. On the other hand, microwaves have higher frequencies and shorter wavelengths.

Explanation: therefore that's why they don't travel faster.  

4 0
2 years ago
How much energy (in Joules) is released when 12.0 g of water cools from 20.0 °C to 11.0 °C? This is a grade 10 question from the
KATRIN_1 [288]

Answer: - 452.088joule

Explanation:

Given the following :

Mass of water = 12g

Change in temperature(Dt) = (11 - 20)°C = - 9°C

Specific heats capacity of water(c) = 4.186j/g°C

Q = mcDt

Where Q = quantity of heat

Q = 12g × 4.186j/g°C × - 9°C

Q = - 452.088joule

7 0
3 years ago
Scientific laws explain_____.
arsen [322]

Howdy! I have your answer:

Scientific laws explain repeated observations that are experimental.

It also describes aspects of the universe.

~sofia

3 0
3 years ago
ONLY ANSWER IF YOU KNOW 100% BRAINLIEST TO THE FIRST CORRECT ANSWER, AND ANSWER ASAP!
saul85 [17]

Answer: Meter and second

5 0
1 year ago
Read 2 more answers
For what angle of projetion is the range is maximum​
VladimirAG [237]

Answer:

46 degrees

Explanation:

8 0
3 years ago
Other questions:
  • The interest rate that the Fed charges banks that borrow money from it is called A. the discount rate. B. the federal rate. C. t
    13·2 answers
  • Can someone help me?
    11·1 answer
  • Analyze the following terms and phrases about solar activity. Select the two that represent correct matches between cause and ef
    6·1 answer
  • Plz help with dis science
    5·1 answer
  • Can someone explain each of these?
    14·1 answer
  • Please help!!!! on both of them this is physics not math
    14·1 answer
  • What is the name of the convection
    11·1 answer
  • Mike rides his horse with a constant speed of 20 km/h. How far can he travel in 4 hours?
    8·1 answer
  • An astronaut is said to be weightless when he/she travels in a satellite. Does it mean that the earth does not attract him/her?​
    5·1 answer
  • Scientists might make a computer model of volcanic eruptions. What is the
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!