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2 years ago

9

What mass needs to be attached to a spring with a force constant of 7N/m in order to make a simple harmonic oscillator oscillate

with a time period of 3s

1 answer:

Alex_Xolod [135]2 years ago

6 0

Answer:

Mass will be 4.437 kg

Explanation:

We have given force constant k = 7 N/m

Time period of oscillation T = 5 sec

So angular frequency $\omega =\frac{2\pi }{T}=\frac{2\times 3.14}{5}=1.256rad/sec$

We know that angular frequency is given by

$\omega =\sqrt{\frac{k}{m}}$

$1.256 =\sqrt{\frac{7}{m}}$

Squaring both side

$1.577 =\frac{7}{m}$

m = 4.437 kg

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A person who climbs up something (e.g., a hill, a ladder, the stairs) from the ground gains potential energy. a person's weight

zhannawk [14.2K]

We are given the following values:

weight w = 240 lb = 1,067.52 N

energy E = 3,000 J

The formula for potential energy is:

E = w h

where h is the height the person has to climb, therefore:

h = 3000 / 1067.52

<span>h = 2.81 m</span>

<span>
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<span>Therefore he has to climb 2.81 meters</span>

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2 years ago

Calculate the acceleration of the body of mass 3kg on which a force of 42N has been applied for 5s

____ [38]

F=ma

42/3 = a
a = 14m/s^2

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2 years ago

A civil engineer wishes to redesign the curved roadway in the example What is the Maximum Speed of the Car? in such a way that a

vlabodo [156]

Answer:

24.3 degrees

Explanation:

A car traveling in circular motion at linear speed v = 12.8 m/s around a circle of radius r = 37 m is subjected to a centripetal acceleration:

$a_c = \frac{v^2}{r} = \frac{12.8^2}{37} = 4.43 m/s^2$

Let α be the banked angle, as α > 0, the outward centripetal acceleration vector is split into 2 components, 1 parallel and the other perpendicular to the road. The one that is parallel has a magnitude of 4.43cosα and is the one that would make the car slip.

Similarly, gravitational acceleration g is split into 2 component, one parallel and the other perpendicular to the road surface. The one that is parallel has a magnitude of gsinα and is the one that keeps the car from slipping outward.

So $gsin\alpha = 4.43cos\alpha$

$\frac{sin\alpha}{cos\alpha} = \frac{4.43}{g} = \frac{4.43}{9.81} = 0.451$

$tan\alpha = 0.451$

$\alpha = tan^{-1}0.451 = 0.424 rad = 0.424*180/\pi \approx 24.3^0$

3 0

2 years ago

A) The current theory of the structure of the Earth, called plate tectonics, tells us that the continents are in constant motion

suter [353]

A) The mass of the continent is $2.5\cdot 10^{21} kg$

B) The kinetic energy is 2016 J

C) The speed of the jogger should be 7.1 m/s

Explanation:

A)

The mass of the continent can be calculated as

$m = \rho V$

where

$\rho = 2800 kg/m^3$ is its density

V is its volume

We have to calculate its volume. We know that the continent is represented as a slab of side 5900 km (so its surface is 5900 x 5900, assuming it is a square) and depth of 26 km, so its volume is:

$V=(5900 km)^2 (26 km)=9.05\cdot 10^8 km^3 =9.05 \cdot 10^8 \cdot (10^9 m^3/k^3)=9.05\cdot 10^7 m^3$

So, the mass of the continent is

$m=\rho V = (2800)(9.05\cdot 10^{17})=2.5\cdot 10^{21} kg$

B)

The kinetic energy of a body is given by

$K=\frac{1}{2}mv^2$

where

m is the mass of the body

v is its speed

For the continent, we have:

$m=2.5\cdot 10^{21} kg$ is the mass

$v=4 cm/year$ is the speed

We have to convert the speed into SI units. we have:

1 cm = 0.01 m

$1 year = (365)(24)(60)(60) s = 3.15\cdot 10^7 s$

So, the speed is

$v=4 cm/year = 0.04 m/year \cdot \frac{1}{3.15\cdot 10^7}=1.27\cdot 10^{-9} m/s$

Therefore, the kinetic energy is

$K=\frac{1}{2}(2.5\cdot 10^{21} kg)(1.27\cdot 10^{-9} m/s)^2=2016 J$

C)

Again, the kinetic energy of an object is

$K=\frac{1}{2}mv^2$

For the jogger in this problem, his mass is

m = 80 kg

And we want its kinetic energy to be equal to that of the continent, so

K = 2016 J

Re-arranging the equation for v, we find what speed the jogger needs to have this kinetic energy:

$v=\sqrt{\frac{2K}{m}}=\sqrt{\frac{2(2016)}{80}}=7.1 m/s$

Learn more about kinetic energy here:

brainly.com/question/6536722

#LearnwithBrainly

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2 years ago

On her way home from work, Brenda drove 20 miles at 60 miles per hour. Due to poor weather conditions, she then reduced her spee

rjkz [21]

Answer:

D

Explanation:

Speed = distance / time

her time for the first journey = 20 miles / 60 miles/hr = 1/3 hr

her time for second part of the journey = her remaining distance / her speed = (80 - 20) miles / 30 miles/hr = 60 miles / 30 miles/hr = 2 hrs

total time spend by her = 2 hr+ 1/3 hr = 2 1/3 hrs

her traveling the distance at 40 miles per hour = 80 miles / 40 miles /hr = 2 hrs

the time less she would drive if she drive the entire distance at 40 miles/hr = 2 1/3 hrs - 2 hrs = 1/3 hr

3 0

2 years ago