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
torisob [31]
3 years ago
5

A horizontal spring is attached to a wall at one end and a mass at the other. The mass rests on a frictionless surface. You pull

the mass, stretching the spring beyond the equilibrium position a distance A, and release it from rest. The mass then begins to oscillate in simple harmonic motion with amplitude A. During one period, the mass spends part of the time in regions where the magnitude of its displacement from equilibrium is greater than (0.66)A— that is, when its position is between −A and(−0.66)A, and when its position is between (0.66)A and A. What total percentage of the period does the mass lie in these regions?
Physics
1 answer:
LenKa [72]3 years ago
6 0

Answer:

54%

Explanation:

So, we have that the "magnitude of its displacement from equilibrium is greater than (0.66)A—''. Thus, the first step to take in answering this question is to write out the equation showing the displacement in simple harmonic motion which is = A cos w×t.

Therefore, we will have two instances t the displacement that is to say at a point 2π/w - a2 and the second point at a = a2.

Let us say that 2π/w = A, then, we have that a = A cos ^-1 (0.66)/2π. Also, we have that a2 = A/2 - A cos^- (0.66) / 2π.

The next thing to do is to calculate or determine the total length of of the required time. Thus, the total length is given as:

2a1 + ( A - 2a2) = 2A{ cos^-1 (0.66)}/ π.

Therefore, the total percentage of the period does the mass lie in these regions = 100 × {2a1 + ( A - 2a2) }/A = 2 { cos^-1 (0.66)}/ π × 100 = 54%.

Thus, the total percentage of the period does the mass lie in these regions = 54%.

You might be interested in
A mass m = 3.9 kg hangs from a massless string wrapped around a uniform cylinder with mass Mp = 10.53 and radius R= 0.96 m. The
luda_lava [24]

Answer:

the rotational inertia of the cylinder = 4.85 kgm²

the mass moved 7.942 m/s

Explanation:

Formula for calculating Inertia can be expressed as:

I =\frac{1}{2}mR^2

For calculating the rotational inertia of the cylinder ; we have;

I = \frac{1}{2}m_pR^2

I = \frac{1}{2}*10.53*(0.96)^2

I=5.265*(0.96)^2

I=4.852224

I ≅ 4.85 kgm²

mg - T ma and RT = I ∝

T = \frac{Ia}{R^2}

a = \frac{g}{1+\frac{I}{mR^2}}

a = \frac{9.8}{1+\frac{4.85}{3.9*(0.96)^2}}

a = 4.1713 m/s²

Using the equation of motion

v^2 = u^2+2as \\ \\ v^2 = 2as \\ \\ v = \sqrt{2*a*s} \\ \\ v= \sqrt{2*4.1713*7.56} \\ \\ v = 7.942 \ m/s

3 0
3 years ago
Read 2 more answers
A baby carriage is sitting at the top of a hill that is 21 m high. The carriage with the baby has a mass of 4kg. The carriage ha
Ira Lisetskai [31]

Answer:

E=252J

Explanation:

The total mechanical energy of an object or system is given by:

E mech=K+U

Where K is the kinetic energy of the object and U is the potential energy of the object. The carriage, sitting motionless at the top of the hill, has only potential energy in the form of gravitational potential energy.

Gravitational potential energy is given by:

Ug=mgh

Where m is the mass of the object, g is the gravitational acceleration constant, and h is the height of the object above some specific reference point, in this case the ground 21 m below.

The weight of a stationary object at the surface of the earth is equal to the force of gravity acting on the object.

W=→Fg=mg

We are given that the carriage weighs 12 N, therefore mg=12N.

Ug=12N⋅21m

⇒Ug=252Nm=252J

Hope it helped, God bless you!

5 0
4 years ago
If a melon has a a mass of 1 kg, how much does the melon weigh?
My name is Ann [436]

Explanation:

1kg = approximately 10N

6 0
2 years ago
If you drop a silver dollar off a building and it hits the ground in 10 seconds, how fast was the coin going just before it hit?
Illusion [34]
Objects in free fall, disregarding terminal velocity, accelerate at 9.8(m/s)/s. so for every second it was falling, it gained 9.8m/s in speed. 9.8 * 10 = 98m/s
4 0
3 years ago
Read 2 more answers
Conductors have ___<br> resistance.
vazorg [7]

Answer:

little/no

Explanation:

Conductors are materials, which conduct electricity and/or heat. That means, that their resistance to such energy is so little, that an electric current is able to pass through.

5 0
3 years ago
Other questions:
  • One of the primary goals of the Kepler space telescope is to search for Earth-like planets. Data gathered by the telescope indic
    6·1 answer
  • What sentence(s) is/are true when we talk about equipotential lines?
    14·1 answer
  • How many revolutions per minute would a 25 m -diameter ferris wheel need to make for the passengers to feel "weightless" at the
    9·1 answer
  • Why is it good for scientist to be skeptical
    9·1 answer
  • The muzzle velocity of an armor-piercing round fired from an M1A1 tank is 1770 m/s (nearly 4000 mph or mach 5.2). A tank is at t
    7·1 answer
  • There are three known forms of uranium. These forms are called _____ of each other.
    10·1 answer
  • HURRY PLEASE!!!
    5·2 answers
  • Sleep is a difficult problem for dolphins because dolphins __________. A. need more sleep than their predators B. must be awake
    5·2 answers
  • On earth, what forces tend to slow an object down?
    10·2 answers
  • TRUE OR FALSE: Aquaponics decreases cost for equipment, energy usage, and land usage. *
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!