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
garri49 [273]
3 years ago
12

A small metal ball is suspended from the ceiling by a thread of negligible mass. The ball is then set in motion in a horizontal

circle so that the thread’s trajectory describes a cone. The acceleration of gravity is 9.8 m/s 2 . How long does it take for the ball to rotate once around the axis?
Physics
1 answer:
Gemiola [76]3 years ago
4 0

Answer:

Time taken, T=2\pi \sqrt{\dfrac{l\ cos\theta}{g}}

Explanation:

It is given that, a small metal ball is suspended from the ceiling by a thread of negligible mass. The ball is then set in motion in a horizontal circle so that the thread’s trajectory describes a cone as shown in attached figure.

From the figure,

The sum of forces in y direction is :

T\ cos\theta-mg=0

T=\dfrac{mg}{cos\theta}

Sum of forces in x direction,

T\ sin\theta=\dfrac{mv^2}{r}

mg\ tan\theta=\dfrac{mv^2}{r}.............(1)

Also, r=l\ sin\theta

Equation (1) becomes :

mg\ tan\theta=\dfrac{mv^2}{l\ sin\theta}

v=\sqrt{gl\ tan\theta.sin\theta}...............(2)

Let t is the time taken for the ball to rotate once around the axis. It is given by :

T=\dfrac{2\pi r}{v}

Put the value of T from equation (2) to the above expression:

T=\dfrac{2\pi r}{\sqrt{gl\ tan\theta.sin\theta}}

T=\dfrac{2\pi l\ sin\theta}{\sqrt{gl\ tan\theta.sin\theta}}

On solving above equation :

T=2\pi \sqrt{\dfrac{l\ cos\theta}{g}}

Hence, this is the required solution.

You might be interested in
In what ways does a stream transport its load, and which part of the load moves most slowly? Select all that apply.
vodka [1.7K]

Answer: Option (B)

Explanation: A stream transports its materials in different ways-

  1. <u>Dissolved load-</u> Here, the materials gets dissolved when mixed with water and flows along with the stream.
  2. <u>Suspended load</u>- Here, the materials are not fully dissolved in the water but they can be carried from one place to another in suspension mode, by the river.
  3. <u>Bed load-</u> Bed load are transported in three different ways such as-
  • Sliding- here, the materials slides down along a curved surface under the water and carried away.
  • Rolling- here, the materials are solid and due to force exerted by water, it can roll and move to distant places.
  • Saltation- here, the materials are carried away in a series of jumps.

Thus, the most appropriate answer is option (B) i.e bedload.

5 0
3 years ago
Technician A says the counter gear is actually several gears machined out of a single piece of steel. Technician B says the coun
dexar [7]

Answer:

Option c. (Both Technician A and B are correct)

Explanation:

A transmission system consists of 3 shafts. The input shaft, the counter shaft, and the main shaft. The clutch gear always rotates with input shaft and is a crucial element of the input shaft.

The counter shaft is actually several gears machined out of a single piece of steel. The counter shaft may also be called counter gear or cluster gear.  It is a secondary shaft that runs parallel to the mainshaft in a gearbox and is used to provide powers to machine components such as the drive axle.

The main gears (also called the speed gears) on main shaft (also known as the output shaft) are used to transfer rotation from counter shaft to the output shaft.

Hence in the light of above description, both technician A and B are correct.

4 0
3 years ago
Read 2 more answers
Someone help please by providing work and answers please :)
cupoosta [38]
There are two ways to solve this. The longer way is to use those equations to calculate numbers for total distance.

The easier way is to find the area under the graph. That's right, AREA UNDER VELOCITY-TIME graph is the TOTAL DISTANCE travelled!

it's a shortcut.

Let's split up the area into a triangle and rectangle:

Triangle = 0.5(4-0)(10-0) = 20 m
Rectangle = (6-4)(10-0) = 20 m

Total distance = 40 m!
6 0
3 years ago
A 20.00 kg lead sphere is hanging from a hook by a thin, massless wire 2.80 m long and is free to swing in a complete circle. Tr
Tema [17]

The minimum initial speed of the dart so that the combination makes a complete circular loop after the collision is 58.5 m/s.

<h3>Minimum speed for the object not fall out of the circle</h3>

The minimum speed if given by tension in the wire;

T + mg = ma

T + mg = m(v²)/R

tension must be zero for the object not fall

0 + mg = mv²/R

v = √(Rg)

<h3>Final speed of the two mass after collision</h3>

Use the principle of conservation of energy

K.Ef  = K.Ei + P.E

¹/₂mvf² = ¹/₂mv² + mg(2R)

¹/₂vf² = ¹/₂v² + g(2R)

¹/₂vf² = ¹/₂(Rg) + g(2R)

vf² = Rg + 4Rg

vf² = 5Rg

vf = √(5Rg)

vf = √(5 x 2.8 x 9.8)

vf = 11.7 m/s

<h3>Initial speed of the dart</h3>

Apply principle of conservation of linear momentum for inelastic collision;

5v = vf(20 + 5)

5v = 11.7(25)

5v = 292.5

v = 58.5 m/s

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

#SPJ1

3 0
1 year ago
When connected to a battery, a lightbulb glows brightly. If the battery is reversed and reconnected to the bulb, the bulb will g
BartSMP [9]
If the battery is reversed and reconnected to the bulb, the bulb will glow <span>with the same brightness. The correct option among all the options that are given in the question is the third option or the penultimate option. I hope that this is the answer that you were looking for and it has actually come to your help.</span>
5 0
3 years ago
Other questions:
  • Why are objects that fall near Earth's surface rarely in free fall?
    11·1 answer
  • Which of the following best describes how galaxies exist in the universe?
    9·2 answers
  • The electric field of a charge is defined by the force on what kind of particle?
    15·1 answer
  • Do all of them please and explain
    15·2 answers
  • Large electric fields in cell membranes cause ions to move through the cell wall. The field strength in a typical membrane is 1.
    5·1 answer
  • PLEASE PLEASE HELP! this is on newton’s 2nd law! i will award 20 points and make you brainliest! ASAP PLEASE! ;)
    5·2 answers
  • SUPER EASY 12 POINTS!!!!! Weather maps contain several standard symbols to convey information about the weather. Explain how to
    7·1 answer
  • What describes the movement of a fluid during convection?
    6·1 answer
  • The distance recorded for riding a motorcycle on its rear wheel without stopping is more than 320 km! Suppose the rider in this
    11·1 answer
  • Lucifer is sitting in a tree that is 15 m above the ground. She jumps straight off the tree in the horizontal direction and land
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!