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Radda [10]
3 years ago
15

A 1.2-kg mass suspended from a spring of spring constant 22 N.m-1 executes simple harmonic motion of amplitude 5 cm. What is the

period T and frequency f of this oscillation? A mass of 1.2 kg attached to a spring is in simple harmonic motion along the x-axis with a period T = 2.5 s. If the total energy of the system is 2.7 J, what is the amplitude of the oscillation? An 8.0-kg block is attached to a spring with a spring constant of . If the spring is stretched 3.0 cm from its equilibrium position and released from rest, the maxium velocity attained by the mass is? Enter question here...
Physics
1 answer:
iren2701 [21]3 years ago
6 0

Answer:

a)  T = 1,467 s , b)    A = 0.495 m , c)  v = 4.97 10⁻² m / s

Explanation:

The simple harmonic movement is described by the expression

        x = A cos (wt + Ф)

Where the angular velocity is

       w = √ k / m

a) Ask the period

Angular velocity, frequency and period are related

      w = 2π f = 2π / T

      T = 2π / w

      T = 2pi √ m / k

      T = 2π √ (1.2 / 22)

      T = 1,467 s

      f = 1 / T

      f = 0.68 Hz

b) ask the amplitude

The mechanical energy of a harmonic oscillator

        E = ½ k A²

       A = √2 E / k

       A = √ (2 2.7 / 22)

       A = 0.495 m

c) the mass changes to 8.0 kg

As released from rest Ф = 0, the equation remains

         x = A cos wt

        w = √ (22/8)

        w = 1,658

         x = 3.0 cos (1,658 t)

Speed ​​is

         v = dx / dt

         v = -A w sin wt

The speed is maximum when without wt = ±1

         v = Aw

         v = 0.03    1,658

         v = 4.97 10⁻² m / s

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Juliette [100K]

Answer:

It traveled 4 centimeters.

Explanation:

In a speed versus time graph, the distance travelled is given by the area under the graph.

In this graph we have the following:

- The speed of the object is v = 1 cm/s between time t = 0 s and t = 4 s

- The speed of the object is v = 0 cm/s between time t = 4 s and t = 8 s

Since the speed in the second part is zero, the distance travelled in the second part is zero. So, the only distance travelled by the object is the distance travelled during the first part, which is equal to the area of the first rectangle:

d=v\Delta t=(1)(4-0)=4 cm

4 0
3 years ago
In the physics lab, a block of mass M slides down a frictionless incline from a height of 35cm. At the bottom of the incline it
bogdanovich [222]

Solution :

Given :

M = 0.35 kg

$m=\frac{M}{2}=0.175 \ kg$

Total mechanical energy = constant

or $K.E._{top}+P.E._{top} = K.E._{bottom}+P.E._{bottom}$

But $K.E._{top} = 0$ and $P.E._{bottom} = 0$

Therefore, potential energy at the top = kinetic energy at the bottom

$\Rightarrow mgh = \frac{1}{2}mv^2$

$\Rightarrow v = \sqrt{2gh}$

      $=\sqrt{2 \times 9.8 \times 0.35}$      (h = 35 cm = 0.35 m)

      = 2.62 m/s

It is the velocity of M just before collision of 'm' at the bottom.

We know that in elastic collision velocity after collision is given by :

$v_1=\frac{m_1-m_2}{m_1+m_2}v_1+ \frac{2m_2v_2}{m_1+m_2}$

here, $m_1=M, m_2 = m, v_1 = 2.62 m/s, v_2 = 0$

∴ $v_1=\frac{0.35-0.175}{0.5250}+\frac{2 \times 0.175 \times 0}{0.525}

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Therefore, velocity after the collision of mass M = 0.33 m/s

 

3 0
3 years ago
Find the moment of inertia Ihoop of a hoop of radius r and mass m with respect to an axis perpendicular to the hoop and passing
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Answer: MR²

is the the moment of inertia  of a hoop of radius R and mass M with respect to an axis perpendicular to the hoop and passing through its center

Explanation:

Since in the hoop , all mass elements  are situated at the same distance from the centre , the following expression for the moment of inertia can be written as follows.

I = ∫ r² dm

= R²∫ dm

MR²

where M is total mass and R is radius of the hoop .

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