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3241004551 [841]
3 years ago
13

Show that the Mass spring system executes simple harmonic motion(SHM)?​

Physics
1 answer:
murzikaleks [220]3 years ago
5 0

Explanation:

Show that the motion of a mass attached to the end of a spring is SHM

Consider a mass "m" attached to the end of an elastic spring. The other end of the spring is fixed

at the a firm support as shown in figure "a". The whole system is placed on a smooth horizontal surface.

If we displace the mass 'm' from its mean position 'O' to point "a" by applying an external force, it is displaced by '+x' to its right, there will be elastic restring force on the mass equal to F in the left side which is applied by the spring.

According to "Hook's Law

F = - Kx ---- (1)

Negative sign indicates that the elastic restoring force is opposite to the displacement.

Where K= Spring Constant

If we release mass 'm' at point 'a', it moves forward to ' O'. At point ' O' it will not stop but moves forward towards point "b" due to inertia and covers the same displacement -x. At point 'b' once again elastic restoring force 'F' acts upon it but now in the right side. In this way it continues its motion

from a to b and then b to a.

According to Newton's 2nd law of motion, force 'F' produces acceleration 'a' in the body which is given by

F = ma ---- (2)

Comparing equation (1) & (2)

ma = -kx

Here k/m is constant term, therefore ,

a = - (Constant)x

or

a a -x

This relation indicates that the acceleration of body attached to the end elastic spring is directly proportional to its displacement. Therefore its motion is Simple Harmonic Motion.

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A ball of mass 2 kg is kept on the hill of height 3 km. Calculate the potential energy possessed by it ?
zysi [14]
We know that -

P.E=m*g*h

Where,

m = mass

g = acceleration due to gravity

h=height

First we convert height into meters.

1 km = 1000 meters

3 km = 1000 * 3 meters = 3000 meters

So, putting the values in the above formula, and by taking 'g' = 9.8 m/s², we get-

P.E.= 2*3000*9.8

P.E.= 58800 Joules

P.E.= 58.8 kJ

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3 years ago
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2 years ago
A 12 n cart is moving on a horizontal surface with a coefficient of kinetic friction of 0.20. what force of friction must be ove
jonny [76]

We must remember that the total net force equation at constant velocity is:

<span>F – Ff = 0</span>

of

F - µN = 0

Using Newton's 2nd Law of Motion:<span>

F = m a 

<span>Where,

F = net force acting on the body 
m = mass of the body 
a = acceleration of the body 

Since the cart is moving at a constant velocity, then acceleration is zero, hence the working equation simplifies to 

F = net Force = 0 

Therefore, 

F - µN = 0 

where 

µ = coefficient of friction = 0.20 
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Therefore, 

F - 0.20(12) = 0 

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4 0
3 years ago
A large pendulum with a 200-lb gold plated bob 12 inches in diameter is on display in the lobby of the united nations building.
BaLLatris [955]
The period of one full swing depends on the length of the pendulum and on gravity. The period of each full swing would be longer on the moon, with less gravity.

The rotation of the plane of the swings doesn't depend on the length of the string OR on gravity. It only depends on the latitude of the place where the pendulum hangs, and the rotation period of the body it's located on.

On Earth, it's (24 hours)/(sine of latitude).

On the moon, it would be (27.32 days)/(sine of latitude).
8 0
3 years ago
Read 2 more answers
(a) An object that has a small mass and an object that has a large mass have the same momentum. Which object has the largest kin
Iteru [2.4K]

Answer:

A) The smaller object; B) The larger object

Explanation:

A) Lets say the small object is 2 kg and the large one is 6 kg. Lets say they also have 30 kg*m/s of momentum each. The small object would have 15 m/s velocity and the large would have 5 m/s.

Now for kinetic energy(.5*m*v²), the small object is .5*2*15², which is 225 J

The large object is .5*6*5², which is 75 J, so the smaller object has more Kinetic energy. Since velocity is squared, it is more important than how large mass is.

B) Same masses as part A. Lets say the kinetic energy is 45 J for both of them. For the small object, 45=.5*2*v²

.5*2 is 1, so 45/1 is 45. Take the square root and we get v= 6.71 m/s

For the large object, 45=.5*6*v²

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Now we plug the velocities into p=mv

For the small object, p=2*6.71, which gives us p=13.42 kg*m/s

For the large object, p=6*3.87, which gives us p=23.22 kg*m/s

The larger object has the larger momentum.

Hope this helps

5 0
3 years ago
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