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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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A -kilogram car travels at a constant speed of 20. meters per second around a horizontal circular track. The diameter of the tra
Tatiana [17]

Answer:

The centripetal acceleration of the car is 8\ m/s^2.

Explanation:

Let the mass of the car, m=10^3\ kg

Diameter of the circular path, d = 100 m

Speed of car, v = 20 m/s

Radius, r = 50 m

When an object moves in a circular path, the centripetal acceleration acts on it. It is given by :

a=\dfrac{v^2}{r}

a=\dfrac{(20\ m/s)^2}{50\ m}

a=8\ m/s^2

So, the centripetal acceleration of the car is 8\ m/s^2. Hence, this is the required solution.

4 0
3 years ago
An insulated thermos contains 106.0 cm3 of hot coffee at a temperature of 80.0 °C. You put in 11.0 g of ice cube at its melting
Andrei [34K]

Answer:

the final temperature is T f = 64.977 ° C≈ 65°C

Explanation:

Since the thermus is insulated, the heat absorbed by the ice is the heat released by the coffee. Thus:

Q coffee + Q ice = Q surroundings =0 (insulated)

We also know that the ice at its melting point , that is 0 °C ( assuming that the thermus is at atmospheric pressure= 1 atm , and has an insignificant amount of impurities ).

The heat released by coffee is sensible heat : Q = m * c * (T final - T initial)

The heat absorbed by ice is latent heat and sensible heat : Q = m * L + m * c * (T final - T initial)

therefore

m co * c co * (T fco - T ico) + m ice * L + m ice * c wat  * (T fwa - T iwa) = 0

assuming specific heat capacity of coffee is approximately the one of water c co = c wa = 4.186 J/g°C and the density of coffee is the same as water

d co = dw = 1 gr/cm³

therefore m co = d co * V co = 1 gr / cm³ * 106 cm³ = 106 gr

m co * c wat * (T f  - T ico) + m ice * L + m ice * c wat  * (T f - T iwa) = 0

m co * c wat * T f+ m ice * c wat  * T f  = m ice * c wat  * T iwa  + m co * c wat * Tico -m ice * L

T f  = (m ice * c wat  * T iwa  + m co * c wat * Tico -m ice * L ) /( m co * c wat * + m ice * c wat )

replacing values

T f = (11 g * 4.186 J/g°C * 0°C +  106 g * 4.186 J/g°C*80°C - 11 g * 334 J/gr) / ( 11 g * 4.186 J/g°C +  106 g * 4.186 J/g°C* ) = 64,977 ° C

T f = 64.977 ° C

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3 years ago
A marble, a bowling ball, a basketball, and a baseball are rolling across the floor at 1.0 m/s. Which one has the greatest kinet
sveticcg [70]

Answer: A Bowling Ball

Explanation:

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K.E = 0.5 mv²

K.E. ∝ m

It is given that the marble, bowling ball, basketball and baseball all are rolling with the same speed. This means that the greatest energy would be possessed by the body having greatest mass.

On an average the mass of a marble is about 50 g, mass of a bowling ball is 750 g, mass of baseball is 150 g and mass of basketball is 600 g. Since the mass of a Bowling ball is the greatest, it would possess the greatest kinetic energy.

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