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saw5 [17]
3 years ago
14

An astronaut measures her mass by means of a device consisting of a chair attached to a large spring.Her mass can be determined

from the period of the oscillations she undergoes when set into motion.If her mass together with the chair is 170 kg, and the spring constant is 1250 N/m, what time is required for her to undergo 10 full oscillations?
Physics
1 answer:
Olenka [21]3 years ago
6 0

Answer:

23 seconds

Explanation:

Step one:

given data

mass m= 170kg

The spring constant is 1250 N/m

Required

The period required for 10 oscillations

Step two:

The expression relating period, mass, and spring constant is

T=2 \pi \sqrt{\frac{m}{k} } \\

substituting our data we have

T=2 *3.142 \sqrt{\frac{170}{1250} } \\\\T=6.284* \sqrt{0.136}\\\\T=6.284*0.3687\\T=2.3s

A Period is defined as the time required to complete one full oscillation

hence, having found the period to be 2.3 seconds, the time required for 10 oscillations will be 2.3*10= 23seconds

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What is the speed of a wave that has a frequency of 125 Hz and a wavelength of 1.25 meters?
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3 years ago
Very far from earth (at R- oo), a spacecraft has run out of fuel and its kinetic energy is zero. If only the gravitational force
Margaret [11]

Answer:

Speed of the spacecraft right before the collision: \displaystyle \sqrt{\frac{2\, G\cdot M_\text{e}}{R\text{e}}}.

Assumption: the earth is exactly spherical with a uniform density.

Explanation:

This question could be solved using the conservation of energy.

The mechanical energy of this spacecraft is the sum of:

  • the kinetic energy of this spacecraft, and
  • the (gravitational) potential energy of this spacecraft.

Let m denote the mass of this spacecraft. At a distance of R from the center of the earth (with mass M_\text{e}), the gravitational potential energy (\mathrm{GPE}) of this spacecraft would be:

\displaystyle \text{GPE} = -\frac{G \cdot M_\text{e}\cdot m}{R}.

Initially, R (the denominator of this fraction) is infinitely large. Therefore, the initial value of \mathrm{GPE} will be infinitely close to zero.

On the other hand, the question states that the initial kinetic energy (\rm KE) of this spacecraft is also zero. Therefore, the initial mechanical energy of this spacecraft would be zero.

Right before the collision, the spacecraft would be very close to the surface of the earth. The distance R between the spacecraft and the center of the earth would be approximately equal to R_\text{e}, the radius of the earth.

The \mathrm{GPE} of the spacecraft at that moment would be:

\displaystyle \text{GPE} = -\frac{G \cdot M_\text{e}\cdot m}{R_\text{e}}.

Subtract this value from zero to find the loss in the \rm GPE of this spacecraft:

\begin{aligned}\text{GPE change} &= \text{Initial GPE} - \text{Final GPE} \\ &= 0 - \left(-\frac{G \cdot M_\text{e}\cdot m}{R_\text{e}}\right) = \frac{G \cdot M_\text{e}\cdot m}{R_\text{e}} \end{aligned}

Assume that gravitational pull is the only force on the spacecraft. The size of the loss in the \rm GPE of this spacecraft would be equal to the size of the gain in its \rm KE.

Therefore, right before collision, the \rm KE of this spacecraft would be:

\begin{aligned}& \text{Initial KE} + \text{KE change} \\ &= \text{Initial KE} + (-\text{GPE change}) \\ &= 0 + \frac{G \cdot M_\text{e}\cdot m}{R_\text{e}} \\ &= \frac{G \cdot M_\text{e}\cdot m}{R_\text{e}}\end{aligned}.

On the other hand, let v denote the speed of this spacecraft. The following equation that relates v\! and m to \rm KE:

\displaystyle \text{KE} = \frac{1}{2}\, m \cdot v^2.

Rearrange this equation to find an equation for v:

\displaystyle v = \sqrt{\frac{2\, \text{KE}}{m}}.

It is already found that right before the collision, \displaystyle \text{KE} = \frac{G \cdot M_\text{e}\cdot m}{R_\text{e}}. Make use of this equation to find v at that moment:

\begin{aligned}v &= \sqrt{\frac{2\, \text{KE}}{m}} \\ &= \sqrt{\frac{2\, G\cdot M_\text{e} \cdot m}{R_\text{e}\cdot m}} = \sqrt{\frac{2\, G\cdot M_\text{e}}{R_\text{e}}}\end{aligned}.

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An apple dropped from the branch of a tree hits the ground in 0.5 s. If the acceleration of the apple during its motion is 10 ms
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Given that,

Time = 0.5 s

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(I). We need to calculate the speed of apple

Using equation of motion

v=u+at

Where, v = speed

u = initial speed

a = acceleration

t = time

Put the value into the formula

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(III). We need to calculate the height of the branch of the tree from the ground

Using equation of motion

s=ut+\dfrac{1}{2}gt^2

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(II). We need to calculate the average velocity during 0.5 sec

Using formula of average velocity

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v_{avg}=\dfrac{x_{f}-x_{i}}{t_{f}-t_{0}}

Where, x_{f}= final position

x_{i} = initial position

Put the value into the formula

v_{avg}=\dfrac{1.25+0}{0.5}

v_{avg}=2.5\ m/s

Hence, (I). The speed of apple is 5 m/s.

(II). The average velocity during 0.5 sec is 2.5 m/s

(III). The height of the branch of the tree from the ground is 1.25 m.

7 0
3 years ago
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