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alekssr [168]
3 years ago
6

A uniform solid sphere of mass M and radius R is free to rotate about a horizontal axis through its center. A string is wrapped

around the sphere and is attached to an object of mass m. Assume that the string does not slip on the sphere. (Use the following as necessary: M, m, and g.) Find the acceleration of the object.
Physics
1 answer:
LenaWriter [7]3 years ago
6 0

Answer:

a = \frac{mg}{m + \frac{2}{5}M}

Explanation:

To calculate the Acceleration and the tension of the object, we start by considering the value of the Tension through its moment of Inertia and Acceleration based on the angular velocity

\tau = I\alpha = Tension(T)*R

And a = \alpha R

Replacing,

T*R = I\alpha = (\frac{2}{5} MR^2)*\frac{a}{R})\\T*R = \frac{2}{5}MaR\\T = \frac{2}{5}Ma

The following forces occur in the body,

mg - T = ma

By this way we have the acceleration

mg - \frac{2}{5}Ma = ma

a(m + \frac{2}{5})M) = mg

a = \frac{mg}{m + \frac{2}{5}M}

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A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. Assume the scenario can be modeled with rig
aleksandr82 [10.1K]

Answer:

The rate of change of the shadow length of a person is 2.692 ft/s

Solution:

As per the question:

Height of a person, H = 20 ft

Height of a person, h = 7 ft

Rate = 5 ft/s

Now,

From Fig.1:

b = person's distance from the lamp post

a = shadow length

Also, from the similarity of the triangles, we can write:

\frac{a + b}{20} = \frac{a}{7}

a = \frac{7}{13}b

Differentiating the above eqn w.r.t t:

\frac{da}{dt} = \frac{7}{13}.\frac{db}{dt}

Now, we know that:

Rate = \frac{db}{dt} = 5\ ft/s

Thus

\frac{da}{dt} = \frac{7}{13}.\times 5 = 2.692\ ft/s

5 0
3 years ago
Consider the uniform electric field E = (8.0ĵ + 2.0 ) ✕ 103 N/C. What is its electric flux (in N · m2/C) through a circular area
cluponka [151]

Answer:

5.09 x 10⁵ Nm²/C

Explanation:

The electric flux φ through a planar area is defined as the electric field Ε times the component of the area Α perpendicular to the field. i.e

φ = E A

From the question;

E = (8.0j + 2.0k) ✕ 10³ N/C

r = radius of the circular area = 9.0m

A = area of a circle = π r²           [Take π = 3.142]

A = 3.142 x 9² = 254.502m²

Now, since the area lies in the x-y plane, only the z-component of the electric field is responsible for the electric flux through the circular area.

Therefore;

φ = (2.0) x 10³ x 254.502

φ = 5.09 x 10⁵ Nm²/C

The electric flux is 5.09 x 10⁵ Nm²/C

4 0
2 years ago
Sarah, who lives in Australia notices that the length of the shadow of the flagpole is getting shorter every day when measured a
Allisa [31]

Answer:

Time zone is one important factor in difference in location and this in turn affects the result of the resolution and rotation of shadow produced from the sun or other illumination.

Therefore someone at a place might see a clear large shadow due to shinny sun reflection and another a small or dull Shadow at same time if the intensity of the sun or lighting source is going down.

Explanation:

The closer a body/object is to a lighting source the larger the shadow it produces, and the farther the body the smaller the shadow produced.

3 0
3 years ago
What would the final temperature be if 8.94 X 10 3 joules of heat were added to 454 grams of copper at 23.0 o C?
ozzi

Answer: 74.1^0C

Explanation:

The quantity of heat required to raise the temperature of a substance by one degree Celsius is called the specific heat capacity.

Q=m\times c\times \Delta T

Q = Heat absorbed=8.94\times 10^3 Joules

m= mass of copper = 454 g

c = specific heat capacity = 0.385J/g^0C

Initial temperature of the copper = T_i = 23.0°C

Final temperature of the water = T_f  = ?

Change in temperature ,\Delta T=T_f-T_i

Putting in the values, we get:

8.94\times 10^3=454\times 0.385\times (T_f-23.0)^0C

T_f=74.1^0C

The final temperature of copper will be 74.1^0C

8 0
3 years ago
What is the measurement of six centimeters equal to?
AlladinOne [14]
Six centimeters equal to about two inches
8 0
3 years ago
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