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Butoxors [25]
3 years ago
11

A force of 960 newtons stretches a spring 4 meters. A mass of 60 kilograms is attached to the end of the spring and is initially

released from the equilibrium position with an upward velocity of 6 m/s. Find the equation of motion.
Physics
1 answer:
Drupady [299]3 years ago
4 0

Answer:

x(t) = - 6 cos 2t

Explanation:

Force of spring = - kx

k= spring constant

x= distance traveled by compressing

But force = mass × acceleration

==> Force = m × d²x/dt²

===> md²x/dt² = -kx

==> md²x/dt² + kx=0   ------------------------(1)

Now Again, by Hook's law

Force = -kx

==> 960=-k × 400

==> -k =960 /4 =240 N/m

ignoring -ve sign k= 240 N/m

Put given data in eq (1)

We get

60d²x/dt² + 240x=0

==> d²x/dt² + 4x=0

General solution for this differential eq is;

x(t) = A cos 2t + B sin 2t   ------------------------(2)

Now initially

position of mass spring

at time = 0 sec

x (0) = 0 m

initial velocity v= = dx/dt=  6m/s

from (2) we have;

dx/dt= -2Asin 2t +2B cost 2t = v(t) --- (3)

put t =0 and dx/dt = v(0) = -6 we get;

-2A sin 2(0)+2Bcos(0) =-6

==> 2B = -6

B= -3

Putting B = 3 in eq (2) and ignoring first term (because it is not possible to find value of A with given initial conditions) - we get

x(t) = - 6 cos 2t

==>  

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What is the purpose of using significant figures? How does it relate to accuracy, precision, resolution, and uncertainty?
Umnica [9.8K]

Answer:

#see solution for details

Explanation:

-Uncertainty refers to an estimate of the amount by which a result may differ from this value,

-Precision refers to how closely repeated measurements agree with each other.

-Accuracy refers to how closely a measured value agrees with the correct value.

-The number of significant figures is the number of digits believed to be correct by the person doing the measuring. Therefore, choosing the correct number of significant figures reduces the deviation from the point of accuracy/uncertainty or precision and thereby reducing margin of error in the ensuing calculations.

7 0
3 years ago
An object with a mass m slides down a rough 370 inclined plane where the coefficient of kinetic friction is 0.20. If the plane i
Svetllana [295]

Answer:

v \approx 9.312\,\frac{m}{s}

Explanation:

The Free Body Diagram of the system is presented in the image attached below. The final speed is determined by means of the Principle of Energy Conservation and the Work-Energy Theorem:

K_{A} + U_{g,A} = K_{B} + U_{g,B} + W_{loss}

K_{B} = K_{A} + U_{g,A}-U_{g,B} - W_{loss}

\frac{1}{2}\cdot m \cdot v^{2} = m\cdot g \cdot s\cdot \sin \theta - \mu_{k}\cdot m \cdot g \cdot s \cos \theta

\frac{1}{2}\cdot v^{2} = g\cdot s \cdot (\sin \theta - \mu_{k}\cdot \cos \theta)

v = \sqrt{2\cdot g \cdot s \cdot (\sin \theta - \mu_{k}\cdot \cos \theta)}

v = \sqrt{2\cdot (9.807\,\frac{m}{s^{2}} )\cdot (10\,m)\cdot (\sin 37^{\textdegree} - 0.2\cdot \cos 37^{\textdegree})}

v \approx 9.312\,\frac{m}{s}

3 0
3 years ago
Which refers to the sum of all the forces that act upon an object?
ElenaW [278]

Answer:

Net force refers to the sum of all the forces that act upon an object.

Explanation:

4 0
3 years ago
A distant galaxy is determined to be 150 million light years distant and moving away from us; using the Hubble law determine its
dlinn [17]

Your question kind of petered out there towards the end and you didn't specify
the terms, so I'll pick my own.

The "Hubble Constant" hasn't yet been pinned down precisely, so let's pick a
round number that's in the neighborhood of the last 20 years of measurements:

             <em>70 km per second per megaparsec</em>.

We'll also need to know that 1 parsec = about 3.262 light years.

So the speed of your receding galaxy is

         (Distance in LY) x (1 megaparsec / 3,262,000 LY) x (70 km/sec-mpsc) =

              (150 million) x  (1 / 3,262,000) x (70 km/sec) =

                                 <em>3,219 km/sec  </em>in the direction away from us (rounded)

4 0
3 years ago
A ball is thrown upward at time t=0 from the ground with an initial velocity of 60 m/s (~ 134 mph). Assume that g = 10 m/s2.At w
Shtirlitz [24]

Answer:

6 second

Explanation:

initial velocity of ball, u = 60 m/s

g = 10 m/s^2

Let the ball takes time t to reach at the maximum height

We know that at maximum height, the velocity of ball is zero.

v = 0 m/s

Use first equation of motion

v = u + gt

0 = 60 - 10 x t

t = 6 second

Thus, the ball takes 6 second to reach to maximum height.

7 0
3 years ago
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