Answer:
The puck moves a vertical height of 2.6 cm before stopping
Explanation:
As the puck is accelerated by the spring, the kinetic energy of the puck equals the elastic potential energy of the spring.
So, 1/2mv² = 1/2kx² where m = mass of puck = 39.2 g = 0.0392 g, v = velocity of puck, k = spring constant = 59 N/m and x = compression of spring = 1.3 cm = 0.013 cm.
Now, since the puck has an initial velocity, v before it slides up the inclined surface, its loss in kinetic energy equals its gain in potential energy before it stops. So
1/2mv² = mgh where h = vertical height puck moves and g = acceleration due to gravity = 9.8 m/s².
Substituting the kinetic energy of the puck for the potential energy of the spring, we have
1/2kx² = mgh
h = kx²/2mg
= 59 N/m × (0.013 m)²/(0.0392 kg × 9.8 m/s²)
= 0.009971 Nm/0.38416 N
= 0.0259 m
= 2.59 cm
≅ 2.6 cm
So the puck moves a vertical height of 2.6 cm before stopping
Answer:
25.33 rpm
Explanation:
M = 100 kg
m1 = 22 kg
m2 = 28 kg
m3 = 33 kg
r = 1.60 m
f = 20 rpm
Let the new angular speed in rpm is f'.
According to the law of conservation of angular momentum, when no external torque is applied, then the angular momentum of the system remains constant.
Initial angular momentum = final angular momentum
(1/2 x M x r^2 + m1 x r^2 + m2 x r^2 + m3 x r^2) x ω =
(1/2 x M x r^2 + m1 x r^2 + m3 x r^2 ) x ω'
(1/2 M + m1 + m2 + m3) x 2 x π x f = (1/2 M + m1 + m3) x 2 x π x f'
( 1/2 x 100 + 22 + 28 + 33) x 20 = (1/2 x 100 + 22 + 33) x f'
2660 = 105 x f'
f' = 25.33 rpm
<span>59.027m/s^2
Centripetal force is give by F = mv^2/r
Since
F = ma
The acceleation accoiated with this centripetal force is
a=v^2/r
the radius is found by r=d/2=5.75m
velocity is found by
v=d/t
distance is the circumference of the circle
c=pi*d=11.5*3.14=36.11m
time=60s/30.6rpm=1.96s
v=36.11/1.96=18.423m/s
plugging this back in to
a=v^2/r=(18.423m/s)^2/5.75m=59.027m/s^2</span>
I understand that sound travels faster in water then in air. Water is a liquid, and air is gas.
Water still has the ability to roll the molecules over each other (so water can flow), it has some flexibility.
But I do not understand how a solid that is inflexible can make sound waves travel faster then in a flexible liquid.
In fact, sound waves travel over 17 times faster through steel than through air.
Sound waves travel over four times faster in water than it would in air.
