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
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}

You might be interested in
Determine the nuclear radius (in fm) for each of the following nuclei.
tekilochka [14]

Answer:

(a) 2.75 fm

(b) 2.89 fm

(c) 4.70 fm

(d) 7.12 fm

Explanation:

For a given element, the radius r of its nuclei is given by;

r = r₀A^{(1/3)}

Where;

A = Atomic mass of the element

r₀ = 1.2 x 10⁻¹⁵m = 1.2fm

Now let's solve for the given elements

(a) ¹²₆C

Carbon element => This has an atomic mass number of 12

Therefore its radius is given by;

r = 1.2  x 12^{1/3}

r = 1.2 x 2.29

r = 2.75 fm

(b) ¹⁴₇N

Nitrogen element => This has an atomic mass number of 14

Therefore its radius is given by;

r = 1.2  x 14^{1/3}

r = 1.2 x 2.41

r = 2.89 fm

(c) ⁶⁰₂₇Co

Cobalt element => This has an atomic mass number of 60

Therefore its radius is given by;

r = 1.2  x 60^{1/3}

r = 1.2 x 3.92

r = 4.70 fm

(d) ²⁰⁸₈₂Pb

Lead element => This has an atomic mass number of 208

Therefore its radius is given by;

r = 1.2  x 208^{1/3}

r = 1.2 x 5.93

r = 7.12 fm

4 0
3 years ago
Which type of rock commonly contains fossils? A. sedimentary B. igneous C. metamorphic D. plutonic
Komok [63]

Answer:

A. Sedimentary

Explanation:

I took the test and got this correct. Hopefully this helps you!

3 0
3 years ago
A ball is falling after rolling off a tall roof<br> The ball has what type of energy.
CaHeK987 [17]

Answer:

Linear and rotational Kinetic Energy + Gravitational potential energy

Explanation:

The ball rolls off a tall roof and starts falling.

Let us first consider the potential energy or more specifically gravitational potential energy (mgh; m = mass of the ball, g = acceleration due to gravity, h = height of the roof). This energy comes because someone or something had to do work to take the ball to the top of the roof against the force of gravity. The potential energy is naturally maximum at the top and minimum when the ball finally reaches the ground.

Now, the ball starts to roll and falls off the roof. It shall continue rotating because of inertia (Newton's first law). This contributes to the rotational kinetic energy (\frac{1}{2}I\omega^2; I=moment of inertia of the ball & \omega = angular velocity).

Finally comes the linear kinetic energy or simply, kinetic energy (\frac{1}{2}mv^2) which is caused due to the velocity v of the ball.

3 0
3 years ago
11. An object moves in circular path with constant speed
Temka [501]

Answer:

B. Is its acceleration constant

Explanation:

Uniform circular motion can be described as the motion of an object in a circle at a constant speed. As an object moves in a circle, it is constantly changing its direction. ... An object undergoing uniform circular motion is moving with a constant speed. Nonetheless, it is accelerating due to its change in direction.

6 0
3 years ago
Harmfful effect of earthquake
Snowcat [4.5K]

Answer:

Death, Destruction, Loss of home

5 0
3 years ago
Read 2 more answers
Other questions:
  • A 75.0 kg ladder that is 3.00 m in length is placed against a wall at an angle theta. The center of gravity of the ladder is at
    9·1 answer
  • Elements heavier than hydrogen are formed when light elements undergo nuclear fusion. Fusion takes place within stars at tempera
    11·2 answers
  • A speeding car is travelling at a constant 30.0 m/s when it passes a stationary police car. If the police car delays for 1.00 s
    12·1 answer
  • Time vs. Position of Battery-Operated Car
    15·1 answer
  • Which are long chains of subunits formed by the process of polymerization? Check all that apply.
    10·2 answers
  • You are driving home from school steadily at 95 km/h fro 130 km. It begins to rainand you slow to 65 km/h. You arrive home after
    7·1 answer
  • Imagine a rock is dropped from the top of a tall building.After 2 seconds of falling the rock is instantaneous speed In approxim
    6·1 answer
  • . A girl runs and jumps horizontally off a platform 10m above a pool with a speed of 4.0m/s. As soon as she leaves the platform,
    6·1 answer
  • Which is an example of a non-contact force?
    8·1 answer
  • Having so much trouble with this : which fact represents evidence for the big bang theory
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!