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2 years ago

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A physics department has a Foucault pendulum, a long-period pendulum suspended from the ceiling. The pendulum has an electric ci

rcuit that keeps it oscillating with a constant amplitude. When the circuit is turned off, the oscillation amplitude decreases by 50% in 37 minutes.
a. What is the pendulum's time constant?

b. How much additional time elapses before the amplitude decreases to 25% of its initial value?

1 answer:

antoniya [11.8K]2 years ago

8 0

Answer:

t=37 mins -> 2220sec

We want "T" which is the pendulum time constant

Using this equation

.5A=Ae^(-t/T)

The .5A is half the amplitude

Take ln of both sides to get ride of Ae

=ln(.5)=-2220/T

Now rearrange to = T

T=-2220/ln(.5) = 3202.78sec / 60 secs = 53.38 mins -> first part of the answer.

The second part is really easy. It took 37 mins to decay half way. meaning to decay another half of 50% which equals 25% it will take an additional 37 mins!

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Question 2 (10 points)

kenny6666 [7]

The force required to slow the truck was -5020 N

Explanation:

First of all, we find the acceleration of the truck, which is given by

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

where

v is the final velocity

u is the initial velocity

t is the time

For the truck in this problem,

v = 11.5 m/s

u = 21.9 m/s

t = 2.88 s

So the acceleration is

$a=\frac{11.5-21.9}{2.88}=-3.6 m/s^2$

where the negative sign means that this is a deceleration.

Now we can find the force exerted on the truck, which is given by Newton's second law:

$F=ma$

where

m = 1390 kg is the mass of the truck

$a=-3.6 m/s^2$ is the acceleration

And substituting,

$F=(1390)(-3.6)=-5004 N$

So the closest answer among the option is -5020 N.

Learn more about acceleration and forces:

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8 0

2 years ago

In the circuit shown, the galvanometer shows zero current. The value of resistance R is :

Tasya [4]

Answer:

its supposed to be (a) 1W

8 0

2 years ago

Which of the following quantities represent mass?

lisabon 2012 [21]

Answer:

Explanation:

a ) 12.0 lbs - mass

b ) .34 g - mass

c ) 120 kg - mass

As lbs , g and kg are units of mass , these things represent mass . lbs is FPS unit of mass and kg is SI unit . g is CGS unit of force .

d ) 1600 kN It represents force because kN or kilonewton is unit of force .

e ) it represents , length or distance because m or metre is unit of length .

f ) 411 cm It represents length or distance because cm is smaller unit of length

g ) 899 MN or million newton . Like d ) It also represents force . Million newton is higher unit of force .

6 0

3 years ago

A student is leaving the lesson and walking to Maths at a speed of 1m/s. He notices that he is late for the lesson and speeds up

MAXImum [283]

Answer:

Acceleration = 0.5 m/s²

Explanation:

Given the following data;

Initial velocity, u = 1m/s

Final velocity, v = 3m/s

Time, t = 4 seconds

To find acceleration;

In physics, acceleration can be defined as the rate of change of the velocity of an object with respect to time.

This simply means that, acceleration is given by the subtraction of initial velocity from the final velocity all over time.

Hence, if we subtract the initial velocity from the final velocity and divide that by the time, we can calculate an object’s acceleration.

Mathematically, acceleration is given by the equation;

$Acceleration (a) = \frac{final \; velocity - initial \; velocity}{time}$

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

Substituting into the equation, we have;

Acceleration = (3 - 1)/4

Acceleration = 2/4

Acceleration = 0.5 m/s²

8 0

2 years ago

A friction-less pulley in the shape of a solid cylinder of mass 2.90 kg and radius 30.0 cm is used to draw water from a well. A

WINSTONCH [101]

Answer:

$s=-38.332m$

Explanation:

From the question we are told that

Cylinder of mass $m=2.90 kg$

Radius $R=30.0 m$

Mass of bucket $M_b= 1.90 kg$

Fall time $T_f= 3.70 seconds$

Generally the tension the bucket is mathematically given by

$T-mg=ma$

For cylinder

$T=I*\alpha$

where

$I=1/2mR^2$

$a=R*\alpha$

Giving

$T=-1/2mR\alpha$

Therefore

$a=\frac{-mg}{m+1/2m}$

$a=\frac{-(1.9*9.81)}{1.9+0.5*(2.9)}$

$a=-5.563880597 \approx -5.6m/s^2$

Generally the Newton's equation for motion is mathematically represented as

$s=ut+1/2at^2$

$s=0(3)+1/2*-5.6*(3.7)^2$

$s=-38.332m$

8 0

2 years ago