Question

Calculate the work required so that a block of mass 5 kg initially at rest and placed on a horizontal frictionless surface, tied by a rope 20 cm long fixed at the other end, begins to rotate until it reaches a speed angular of 2 rps. Do you need to add more work to maintain this speed? Justify your answer by applying the principle of conservation of energy.

67

likes
335 views

Answer to a math question Calculate the work required so that a block of mass 5 kg initially at rest and placed on a horizontal frictionless surface, tied by a rope 20 cm long fixed at the other end, begins to rotate until it reaches a speed angular of 2 rps. Do you need to add more work to maintain this speed? Justify your answer by applying the principle of conservation of energy.

Expert avatar
Hester
4.8
116 Answers
## Treball necessari per girar el bloc Podem analitzar aquest problema utilitzant els conceptes d'inèrcia rotacional, energia cinètica i principi de conservació de l'energia. **Donat:** * Massa del bloc (m) = 5 kg * Longitud de la corda (L) = 20 cm = 0,2 m (convertit a metres) * Velocitat angular final (ω_f) = 2 rad/s **Càlculs:** 1. **Moment d'inèrcia (I):** Com que el bloc gira al voltant d'un extrem de la corda, actua com una massa puntual a l'extrem d'una vareta. El moment d'inèrcia (I) d'aquest sistema és: I = mL^2 I = (5 kg) * (0,2 m)^2 I = 0,2 kgm^2 2. **Energia cinètica (KE):** Un cop el bloc comença a girar, guanya energia cinètica. L'energia cinètica d'un objecte en rotació és: KE = 1/2 * I * ω_f^2 KE = 1/2 * (0,2 kgm^2) * (2 rad/s)^2 KE = 0,4 J 3. **Treball fet (W):** Suposant que no hi ha pèrdua d'energia per fricció, el treball realitzat (W) per fer girar el bloc és igual a l'energia cinètica final guanyada. W = KE W = 0,4 J ## Mantenint la velocitat **No es requereix cap treball addicional per mantenir la velocitat angular de 2 rps un cop aconseguit.** Heus aquí per què, basant-nos en el principi de conservació de l'energia: * **Conservació de l'energia mecànica:** Aquest principi estableix que l'energia mecànica total (energia cinètica + energia potencial) en un sistema tancat es manté constant. * **Inicial i finalの状態 (joutai, estat):** Inicialment, el bloc està en repòs sobre una superfície horitzontal. Per tant, la seva energia cinètica és zero. Pot tenir una mica d'energia potencial a causa de la seva posició relativa a un punt de referència, però això no és rellevant aquí ja que la superfície és horitzontal. L'estat final té el bloc girant amb energia cinètica (0,4 J) però sense canvis en l'energia potencial. * **Sense pèrdua d'energia:** Com que la superfície no té fricció, no hi ha dissipació d'energia a causa de la fricció. Per tant, segons el principi de conservació de l'energia, una vegada que el bloc assoleixi una velocitat angular de 2 rps i la seva energia cinètica esdevingui 0,4 J, mantindrà aquesta velocitat indefinidament sense cap entrada de treball addicional sempre que el sistema romangui sense fricció i tancat (és a dir, , no hi actuen forces externes).

Frequently asked questions (FAQs)
Math question: What is the limit as x approaches 3 of (x^2 + 2x - 1)/(x - 3)?
+
What is the value of x if log(base 2)(x+4) = 3?
+
Question: What is the derivative of F(x) = ∫[a to x] f(t) dt, where f(x) = 3x^2 + 2x?
+
New questions in Mathematics
Convert the following function from standard form to vertex form f(x) = x^2 + 7x - 1
Solve: −3(−2x+23)+12=6(−4x+9)+9.
the value of sin 178°58'
What is the amount of interest of 75,000 at 3.45% per year, at the end of 12 years and 6 months?
I need .23 turned into a fraction
Consider numbers from 1 to 2023. We delete 3 consecutive numbers so, that the avarage of the left numbers is a whole number
The bus one way of the road which is 10km is heading with speed of 20km/h ,then the bus the other 10km is heading with speed of 60km/h. The middle speed of the road is it equal with arithmetic speed of the v1 and v2 ?
The beta of a company is 1.51 while its financial leverage is 27%. What is then its unlevered beta if the corporate tax rate is 40%? (4 decimal places)
Perpetual annuities are a series of payments whose duration has no end. Explain how can we calculate them, if they have no end?
What is the appropriate measurement for the weight of an African elephant?
Suppose you have a sample of 100 values from a population with mean mu = 500 and standard deviation sigma = 80. Given that P(z < −1.25) = 0.10565 and P(z < 1.25) = 0.89435, the probability that the sample mean is in the interval (490, 510) is: A)78.87% B)89.44% C)10.57% D)68.27%
sin 30
In a laboratory test, it was found that a certain culture of bacteria develops in a favorable environment, doubling its population every 2 hours. The test started with a population of 100 bacteria. After six hours, it is estimated that the number of bacteria will be:
Congratulations, you have saved well and are ready to begin your retirement. If you have $1,750,000.00 saved for your retirement and want it to last for 40 years, and will earn 10.8% compounded monthly: What is the amount of the monthly distribuion? 216.50 How much interest is earned in retirement?
Let x be an integer. Prove that x^2 is even if and only if is divisible by 4.
16.What payment (deposit) made at the end of each month will accumulate to $10473 in 13 years at 7.9% compounded monthly? Enter to the nearest cent (two decimals). Do not use $ signs or commas in the answer.
A multiple choice exam is made up of 10 questions; Each question has 5 options and only one of them is correct. If a person answers at random, what is the probability of answering only 3 good questions?
The mass of 120 molecules of X2C4 is 9127.2 amu. Identify the unknown atom, X, by finding the atomic mass. The atomic mass of C is 12.01 amu/atom
X^X =49 X=?
Find the set of points formed by the expression 𝜋<|𝑧−4+2𝑖|<3𝜋.