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maw [93]
2 years ago
10

A solid sphere rolls along a horizontal, smooth surface at a constant linear speed without slipping. What is the ratio between t

he rotational kinetic energy about the center of the sphere and the sphere’s total kinetic energy?.
Physics
1 answer:
Pavlova-9 [17]2 years ago
3 0

The ratio of the rotational kinetic energy about the center of the sphere and the total kinetic energy of the sphere is 2/7.

<h3>What is the rotational kinetic energy of a sphere?</h3>

The rotational kinetic energy of the sphere is directly proportional to the square of angular acceleration.

K = \dfrac 12 I\omega ^2

Where,

I = rotational inertia of sphere = 2/5MR²

Where M is the mass of the sphere and R is the radius of the sphere,

ω = angular acceleration of sphere = V/R

Where V is the speed of the sphere.

So,

K = 1/2 × 2/5MR² × V²/R²

K = MV²/5

The translational kinetic energy of the sphere,

K' = \dfrac 12 MV^2

The total kinetic energy of the sphere,

K_t = K + K'

So,

K_t= \dfrac {MV^2}5 +\dfrac { MV^2}2\\\\K_t= \dfrac {7MV^2}{10}

Thus the Ratio of rotational kinetic energy to total kinetic energy,

\dfrac KK_t = \dfrac {\dfrac {MV^2}{5} }{ \dfrac {7MV^2}{10}}\\\\\dfrac KK_t = \dfrac 15 \times \dfrac { 10}7\\\\\dfrac KK_t= \dfrac 27

Therefore, the ratio of the rotational kinetic energy about the center of the sphere and the total kinetic energy of the sphere is 2/7.

Learn more about rotational kinetic energy:

brainly.com/question/14611300

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3 years ago
A volleyball player's hand applies a 39 N force while in contact with a volleyball for 2 seconds. What is the impulse on the bal
antiseptic1488 [7]

Answer:78 N

Explanation:Impulse=Force*time

=39*2 =78 Ns

8 0
3 years ago
18. Un avión de rescate de animales que vuela hacia el este a 36.0 m/s deja caer una paca de
Alona [7]

Answer:

Definimos momento como el producto entre la masa y la velocidad

P = m*v

(tener en cuenta que la velocidad es un vector, por lo que el momento también será un vector)

Sabemos que el peso de la paca de heno es 175N, y el peso es masa por aceleración gravitatoria, entonces.

Peso = m*9.8m/s^2 = 175N

m = (175N)/(9.8m/s^2) = 17.9 kg

Ahora debemos calcular la velocidad de la paca justo antes de tocar el suelo.

Sabemos que la velocidad horizontal será la misma que tenía el avión, que es:

Vx = 36m/s

Mientras que para la velocidad vertical, usamos la conservación de la energía:

E = U + K

Apenas se suelta la caja, esta tiene velocidad cero, entonces su energía cinética será cero y la caja solo tendrá energía potencial (Si bien la caja tiene velocidad horizontal en este punto, por la superposición lineal podemos separar el problema en un caso horizontal y en un caso vertical, y en el caso vertical no hay velocidad inicial)

Entonces al principio solo hay energía potencial:

U = m*g*h

donde:

m = masa

g = aceleración gravitatoria

h = altura  

Sabemos que la altura inicial es 60m, entonces la energía potencial es:

U = 175N*60m = 10,500 N

Cuando la paca esta próxima a golpear el suelo, la altura h tiende a cero, por lo que la energía potencial se hace cero, y en este punto solo tendremos energía cinética, entonces:

10,500N = (m/2)*v^2

De acá podemos despejar la velocidad vertical justo antes de golpear el suelo.

√(10,500N*(2/ 17.9 kg)) = 34.25 m/s

La velocidad vertical es 34.25 m/s

Entonces el vector velocidad se podrá escribir como:

V = (36 m/s, -34.25 m/s)

Donde el signo menos en la velocidad vertical es porque la velocidad vertical es hacia abajo.

Reemplazando esto en la ecuación del momento obtenemos:

P = 17.9kg*(36 m/s, -34.25 m/s)  

P = (644.4 N, -613.075 N)

6 0
3 years ago
Which statement is true for objects in dynamic equilibrium?
lakkis [162]

Answer:

The correct answer to the question is objects have zero acceleration.

Explanation:

Before answering the question, first we have to understand dynamic equilibrium .

A body moving with uniform velocity is said to be in dynamic equilibrium if the net external forces acting on the body is zero. Hence, the body is under balanced forces.

If the external forces acting on a body is not balanced, then the body will accelerate which will destroy its equilibrium condition. Hence, the necessary and sufficient condition for a body to be in dynamic equilibrium is that the forces are balanced.

When a body is in dynamic equilibrium, the body moves with uniform velocity along a straight line unless and until it is compelled by some external unbalanced forces.

Hence, the rate of change of velocity or acceleration of the body will be zero.

5 0
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Mice21 [21]

The distance traveled by the hockey player is 0.025 m.

<h3>The principle of conservation of linear momentum;</h3>
  • The principle of conservation of linear momentum states that, the total momentum of an isolated system is always conserved.

The final velocity of the hockey play is calculated by applying the principle of conservation of linear momentum;

m_1v_1 = m_2 v_2\\\\v_1 = \frac{m_2 v_2}{m_1} \\\\v_1 = \frac{0.150 \times 45}{90} \\\\v_1 = 0.075 \ m/s

The time taken for the puck to reach 15 m is calculated as follows;

t = \frac{d}{v} \\\\t = \frac{15\ m}{45 \ m/s} \\\\t = 0.33 \ s

The distance traveled by the hockey player at the calculated time is;

d = vt\\\\d = 0.075 \ m/s \ \times 0.33 \ s\\\\d = 0.025 \ m

Learn more about conservation of linear momentum here: brainly.com/question/7538238

4 0
2 years ago
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