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
Elden [556K]
3 years ago
5

One end of a thin rod is attached to a pivot, about which it can rotate without friction. Air resistance is absent. The rod has

a length of 0.80 m and is uniform. It is hanging vertically straight downward. The end of the rod nearest the floor is given a linear speed v0, so that the rod begins to rotate upward about the pivot. What must be the value of v0, such that the rod comes to a momentary halt in a straight-up orientation, exactly opposite to its initial orientation?
Physics
1 answer:
Mars2501 [29]3 years ago
4 0

Answer:

6.86 m/s

Explanation:

This problem can be solved by doing the total energy balance, i.e:

initial (KE + PE)  = final (KE + PE). { KE = Kinetic Energy and PE = Potential Energy}

Since the rod comes to a halt at the topmost position, the KE final is 0. Therefore, all the KE initial is changed to PE, i.e, ΔKE = ΔPE.

Now, at the initial position (the rod hanging vertically down), the bottom-most end is given a velocity of v0. The initial angular velocity(ω) of the rod is given by ω = v/r , where v is the velocity of a particle on the rod and r is the distance of this particle from the axis.

Now, taking v = v0 and r = length of the rod(L), we get ω = v0/ 0.8 rad/s

The rotational KE of the rod is given by KE = 0.5Iω², where I is the moment of inertia of the rod about the axis of rotation and this is given by I = 1/3mL², where L is the length of the rod. Therefore, KE = 1/2ω²1/3mL² = 1/6ω²mL². Also, ω = v0/L, hence KE = 1/6m(v0)²

This KE is equal to the change in PE of the rod. Since the rod is uniform, the center of mass of the rod is at its center and is therefore at a distane of L/2 from the axis of rotation in the downward direction and at the final position, it is at a distance of L/2 in the upward direction. Hence ΔPE = mgL/2 + mgL/2 = mgL. (g = 9.8 m/s²)

Now, 1/6m(v0)² = mgL ⇒ v0 = \sqrt{6gL}

Hence, v0 = 6.86 m/s

You might be interested in
An object is falling from a height of 7.5 meters. At what height will it’s velocity be 7 meters/second?
Nady [450]
One of the equations of gravity is this:
{v}^{2} = {u}^{2} + 2gh
Where v = final velocity which is 7m/s
u = initial velocity which is 0 for objects falling from a height
g = acceleration due to gravity and it is approximately 10m/s^2. It's a constant so pretty much remember this number. It's positive since the work being done is caused by gravity (in other words, it's falling down). It can also be negative if the work being down is against gravity (in other words, it's going up)
h = height of object

Substitute for the values and you should have something like this
{7}^{2} = {0}^{2} + 2 \times 10 \times h
49 = 0 + 20h
h = \frac{49}{20}
h = 2.5m
6 0
3 years ago
What is the direction of the normal contact force of the road on the wheels?
Gekata [30.6K]

Answer:

The direction of the contact forces acting on a body is not necessarily perpendicular to the contact surface. The resolution of contact forces in two components i.e. perpendicular to contact surface and along surface. Perpendicular component is normal force and parallel component is friction.

Explanation:

3 0
2 years ago
Which type of energy is transferred by convection currents?
Masteriza [31]
Answer: thermal

Explanation:
Moving particles transfer thermal energy through a fluid by forming convection currents.
7 0
3 years ago
Read 2 more answers
A block of mass 10.0 kg is pulled to the right along a rough horizontal surface with a constant horizontal force of 20.0 N. The
Yakvenalex [24]

Answer:

the magnitude of acceleration will be 1.50m/s^2

Explanation:

To calculate your acceleration, you can use your formula that states that the net force on an object is equal to the mass of the object multiplied by the acceleration of the object. Fnet=ma

if you draw out this situation and label the forces you will have your vector towards the right with a magnitude of 20.0N and then your friction vector will be pointing to the left (in other words, in the negative direction) (opposing the direction of movement) with a magnitude of 5.00N, with the 10.0 kg box in the middle.

The net force will be calculated using F1+F2=Fnet where your F1=20.0N and F2= -5.00N (since it is towards the negative direction).

you will find that Fnet=15.0N

With that, plug in the values you know to calculate the acceleration of the block:

Fnet=ma

(15.0N)=(10.0kg)a    from her you can divide both sides by 10 to isolate a:

1.50=a  (and now make sure to label the units of your answer)

a=1.50m/s^2 (which is the typical unit for acceleration)

7 0
2 years ago
What is happening to the ATOMS INSIDE of a magnet that gives the
Sliva [168]

Answer:

The atoms are aligned in a particular direction

Explanation:

The atoms become aligned in a particular direction in regions called domains, thus resulting in an overall resultant magnetism due to the spin of the electrons.

7 0
2 years ago
Other questions:
  • i) A 100 W and 60 W bulb are joined in series and connected to the mains. Which bulb will glow brighter? Why? ii) A 100 W and a
    7·1 answer
  • How to solve for average speed
    5·1 answer
  • PLEASE HELP WILL GIVE BRAINLIEST
    5·1 answer
  • There is more land in the Northern Hemisphere than in the Southern Hemisphere. How might this difference affect CO2, concentrati
    6·1 answer
  • How many drops of water are in a 1.0 L bottle? (Hint: Start by estimating the diameter of a drop of water.)
    12·2 answers
  • Why do scientists believe that light is made of waves?
    14·1 answer
  • A train accelerated from rest to a speed of 60m/s in 200 seconds it continues with the speed reached for 40 seconds before comin
    7·1 answer
  • Which type of radioactive decay has a positive charge?
    9·1 answer
  • F. If heat could flow to the container, how would the final temperature be affected?
    15·1 answer
  • light of wavelength 3.0 × 10−7 m shines on the metals lithium, iron, and mercury, which have work functions of 2.3 ev, 3.9 ev, a
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!