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
Setler79 [48]
3 years ago
7

Two simple pendulum of slightly different length , are set off oscillating in step is a time of 20s has elasped , during which t

ime the longer pendulum has completed exactly 10 oscillations .Find the length of each pendulum.
Physics
1 answer:
adell [148]3 years ago
6 0

Answer:

Length of longer pendulum = 99.3 cm

Length of shorter pendulum = 82.2 cm

Explanation:

Since the longer pendulum undergoes 10 oscillations in 20 s, its period T = 20 s/10 = 2 s.

From T = 2π√(l/g), the length of the pendulum. l = T²g/4π²

substituting T = 2s and g = 9.8 m/s² we have

l = T²g/4π²

= (2 s)² × 9.8 m/s² ÷ 4π²

= 39.2 m ÷ 4π²

= 0.993 m

= 99.3 cm

Now, for the shorter pendulum to be in step with the longer pendulum, it must have completed some oscillations more than the longer pendulum. Let x be the number of oscillations more in t = 20 s. Let n₁ = number of oscillations of longer pendulum and n₂ = number of oscillations of longer pendulum.

So, n₂ = n₁ + x. Also n₁ = t/T₁ and n₂ = t/T₂ where T₂ = period of shorter pendulum.

t/T₂ = t/T₁ + x

1/T₂ = 1/T₁ + x  (1)

Also, the T₂ = t/n₂ = t/(n₁ + x)  (2)

From (1) T₂ = T₁/(T₁ + x) (3)

equating (2) and (3) we have

t/(n₁ + x) = T₁/(T₁ + x)

substituting t = 20 s and n₁ = 10 and T₁ = 2s, we have

20 s/(10 + x) = 2/(2 + x)

10/(10 + x) = 1/(2 + x)

(10 + x)/10 = (2 + x)

(10 + x) = 10(2 + x)

10 + x = 20 + 10x

collecting like terms

10x - x = 20 - 10

9x = 10

x = 10/9

x = 1.11

x ≅ 1 oscillation

substituting x into (2)

T₂ = t/n₂ = t/(n₁ + x)

= 20/(10 + 1)

= 20/11

= 1.82 s

Since length l = T²g/4π²

substituting T = 1.82 s and g = 9.8 m/s² we have

l = T²g/4π²

= (1.82 s)² × 9.8 m/s² ÷ 4π²

= 32.46 m ÷ 4π²

= 0.822 m

= 82.2 cm

You might be interested in
A bicyclist, initially at rest, begins pedaling and gaining speed steadily for 4.90s during which she covers 25.0m.
emmasim [6.3K]

The bicyclist accelerates with magnitude <em>a</em> such that

25.0 m = 1/2 <em>a</em> (4.90 s)²

Solve for <em>a</em> :

<em>a</em> = (25.0 m) / (1/2 (4.90 s)²) ≈ 2.08 m/s²

Then her final speed is <em>v</em> such that

<em>v</em> ² - 0² = 2<em>a</em> (25.0 m)

Solve for <em>v</em> :

<em>v</em> = √(2 (2.08 m/s²) / (25.0 m)) ≈ 10.2 m/s

Convert to mph. If you know that 1 m ≈ 3.28 ft, then

(10.2 m/s) • (3.28 ft/m) • (1/5280 mi/ft) • (3600 s/h) ≈ 22.8 mi/h

8 0
2 years ago
11. A cyclist accelerates from 0 m/s to 10 m/s in 3 seconds. What is his acceleration ? Is this acceleration higher than that of
Marat540 [252]

a =  \frac{v - u}{t}

v = final velocity

u = initial velocity

t = time taken

the acceleration of the cyclist is

\frac{10 - 0}{3}  = 3.333333....

approximately 3.33 m/s^2

the acceleration of the car is

\frac{40 - 0 }{8}  = 5.0

5.0 m/s^2

5.0 > 3.33 \\ so \:  the \: answer  \: is \: no

6 0
3 years ago
When a wave is acted upon by an external damping force what happens to the energy of the wave
Nimfa-mama [501]

Answer:

A-the energy of the wave decreases gradually

Explanation:

when a wave is acted upon by an external damping force the energy of the wave decreases gradually.

The energy degrades into the form of heat which is considered to be of less value and use. The reason is because it disperses and spreads more widely.

So therefore it end up as heat with a little sound but that is close to none because that too disperses into heat i.e. decreased form of energy.

4 0
3 years ago
The universal force that is effective over the longest distance is called?
gulaghasi [49]
The answer is D. gravity
3 0
3 years ago
Boat A and Boat B have the same mass. Boat A’s velocity is three times greater than that of Boat B. Compared to the kinetic ener
Helen [10]

Answer:

Explanation:

D. Nine times as much.

3 0
3 years ago
Read 2 more answers
Other questions:
  • Suppose that you're facing a straight current-carrying conductor, and the current is flowing toward you.
    13·2 answers
  • Maisie drags a 1kg mass along a table with a Newton meter so that it accelerates at 0.25 m/s. The Newton-meter reads 0.4N, calcu
    5·1 answer
  • An airplane is flying at a constant velocity through the air. What is the relationship between the magnitudes of the four forces
    12·1 answer
  • The trough of the sine curve used to represent a sound wave corresponds to
    15·1 answer
  • The height of the tide measured at a seaside community varies according to the number of hours t after midnight. If the height h
    10·1 answer
  • 26. The ice on the front windshield of the car had formed when moisture condensed during the night. The ice melted quickly after
    12·1 answer
  • I WILL GIVE BRAINLIEST!!!
    14·1 answer
  • What is the name of the process that plants use to remove carbon dioxide from the atmosphere?
    12·2 answers
  • Which 2 points are unbalanced??
    7·1 answer
  • Which quote best reveals why sowers was successful in achieving her goal?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!