If there was any way to do that, then your teacher wouldn't
need to keep you coming into class every day and doing
homework every night. She could just give you the 3 or 4
paragraphs and a few pictures that you're asking me for,
and bada-bing ! you'd know it !
The time it takes, and the amount of homework it takes, is
EXACTLY the time you spent hearing about it in class.
(Unless you're some kind of genius savant prodigy, which
you're not and I'm not.)
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.
Yes it does, uh huh. It slows down as it rolls. That's a fact.
In order for the ball to roll forward, it has to push grass out of the way. That takes energy. To bend each blade of grass out of its way, the ball has to use a tiny bit of the kinetic energy that it has, so it gradually runs out of kinetic energy. When its kinetic energy is all gone, it stops moving.
Answer:
Explanation:
Given that,
Mass attached m = 0.95kg
Spring constant k = 16N/m
Instantaneous speed v = 36cm/s = 0.36m/s
Amplitude A=?
When x = 0.7A
Using conservation of energy
∆K.E + ∆P.E = 0
K.E(final) — K.E(initial) + P.E(final) — P.E(initial) = 0
At the beginning immediately the hammer hits the mass, the potential energy is 0J, Therefore, P.E(initial) = 0J, so the speed is maximum.
Also, at the end, at maximum displacement, the speed is zero, therefore, K.E(final) = 0
So, the equation becomes
— K.E(initial) + P.E(final) = 0
K.E(initial) = P.E(final)
½mv² = ½kA²
mv² = kA²
0.95 × 0.36² = 16×A²
0.12312 = 16•A²
A² = 0.12312/16
A² = 0.007695
A = √0.007695
A = 0.088 m
A = 8.8cm
B. Speed at x = 0.7A
Using the same principle above
K.E(initial) = P.E(final)
½mv² = ½kA²
Where A = 0.7A = 0.7 × 0.088 = 0.0614m
Then,
½× 0.95 × v² = ½ × 16 × 0.0614²
0.475v² = 0.0310644
v² = 0.0310644/0.475
v² = 0.0635
v = √0.0635
v = 0.252 m/s
v = 25.2 cm/s
