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eduard
4 years ago
9

A particle with a mass of 2.3 × 10-20 kg is oscillating with simple harmonic motion with a period of 3.0 × 10-5 s and a maximum

speed of 2.2 × 103 m/s. Calculate (a) the angular frequency and (b) the maximum displacement of the particle.
Physics
1 answer:
baherus [9]4 years ago
8 0

Answer:

angular frequency is 209439.51 rad/sec

maximum displacement  is 0.010504 m

Explanation:

Given data

mass = 2.3 × 10^-20 kg

period = 3.0 × 10^-5 s

maximum speed = 2.2 × 10^3 m/s

to find out

the angular frequency and  maximum displacement

solution

we know angular frequency formula that is

angular frequency = 2 π / period

put here period value we get angular frequency

angular frequency = 2 π / 3.0 × 10^-5

angular frequency is 209439.51 rad/sec

maximum displacement formula is

speed = angular frequency × maximum displacement

put all value and we get maximum displacement

maximum displacement  = 2.2 × 10^3 / 209439.51  

maximum displacement  is 0.010504 m

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A toy plane is flying in a horizontal circle by being attached to a 0.75 meter string. The plane has a mass of 101.7 grams and m
nadezda [96]

Answer:

F = 2,894 N

Explanation:

For this exercise let's use Newton's second law

      F = m a

The acceleration is centripetal

     a = v² / r

Angular and linear variables are related.

     v = w r

Let's replace

     F = m w² r

The radius r and the length of the rope is related

    cos is = r / L

    r = L cos tea

Let's replace

    F = m w² L cos θ

Let's reduce the magnitudes to the SI system

     m = 101.7 g (1 kg / 1000g) = 0.1017 kg

      θ = 5 rev (2π rad / rev) = 31,416 rad

     w =  θ / t

     w = 31.416 / 5.1

     w = 6.16 rad / s

     F = 0.1017 6.16² 0.75 cos  θ

     F = 2,894 cos  θ

The maximum value of F is for  θ equal to zero

     F = 2,894 N

7 0
3 years ago
A child bounces in a harness suspended from a door frame by three elastic bands. If each elastic band stretches 0.300 m while su
WINSTONCH [101]

Answer:

The force constant for each elastic band is 77.93 N/m

Explanation:

Hooke's law of a spring or an elastic band gives the relation between elastic force (Fe) and stretching (x), the magnitude of that force is:

F_{e}= kx (1)

With k, the elastic force constant. The three elastic bands support the child’s weight (W) and maintain him at rest, so by Newton’s second law for one of the elastic bands:

\sum F=0 (2)

\frac{W}{3}-F_{e}=0\Rightarrow F_{e}=\frac{W}{3} (3)

Using (1) on (3):

kx=\frac{W}{3}\Rightarrow k=\frac{mg}{3x}(4)

k=\frac{7.15\,kg*9.81\,\frac{m}{s^{2}}}{3*0.300\,m}\simeq\mathbf{77.93\frac{N}{m}}

8 0
3 years ago
Four long parallel wires each carry 2.0 A in the same direction. They are parallel to the z-axis, and they pass through the corn
yarga [219]

Answer:

A

Explanation:

6 0
3 years ago
A train traveling at 27.5 m/s accelerates to 42.4 m/s over 75.0 s. What is the displacement of the train in this time period
Sergio [31]

Answer:

2621.25 meters

Explanation:

First, write down what we are given.

Initial velocity = 27.5 m/s

Final velocity = 42.4 m/s

Time = 75 seconds

We need to look at the kinematic equations and determine which one will be best.  In this case, we need an equation with distance.  I am going to use v_{f}^{2} = v_{i}^{2} +2ad, but you can also use the other equation, x = v_{o}t+\frac{1}{2}at^{2}

We need to find acceleration.  To find it, we need to use the formula for acceleration: a = \frac{v_{f}-v_{i}}{t}.  Plugging in values, a = \frac{42.4-27.5}{75} = .199\ m/s^{2}

Next, plug in what we know into the kinematics equation and solve for distance.  42.4^{2} = 27.5^{2} + 2(.199)(d)\\d = 2621.25\ meters

7 0
3 years ago
Calculate the angular velocity and linea­r velocity of both wheels assuming the l­arger wheel rotates at 120 revolutions p­er mi
IRINA_888 [86]
<span>120 revolutions p­er min is (20RPM)
120revolutions is 240 Pi radians (because 1 revolution is 2Pi rad)

angular velocity
w= 240Pixf, f is the frequency and f= 1/T, T =1mn=60s=period, so f=1/60=0.01Hz
so w = 240*Pi*0.01=12.56 rad /s
linear velocity can be found with
V =Rx w,    
V=12.56 R the value depends on what value is the radius of both wheels

</span>
6 0
3 years ago
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