Force of friction=75 N
Explanation:
we use Newton's second law of motion
F- Ff= ma
F = applied force=250 N
Ff= force of friction
a= acceleration= 5.83 m/s²
m= mass=30 kg
250- Ff= 30 (5.83)
Ff=250-30(5.83)
Ff=250-175
Ff=75 N
Answer:
0.893 rad/s in the clockwise direction
Explanation:
From the law of conservation of angular momentum,
angular momentum before impact = angular momentum after impact
L₁ = L₂
L₁ = angular momentum of bullet = + 9 kgm²/s (it is positive since the bullet tends to rotate in a clockwise direction from left to right)
L₂ = angular momentum of cylinder and angular momentum of bullet after collision.
L₂ = (I₁ + I₂)ω where I₁ = rotational inertia of cylinder = 1/2MR² where M = mass of cylinder = 5 kg and R = radius of cylinder = 2 m, I₂ = rotational inertia of bullet about axis of cylinder after collision = mR² where m = mass of bullet = 0.02 kg and R = radius of cylinder = 2m and ω = angular velocity of system after collision
So,
L₁ = L₂
L₁ = (I₁ + I₂)ω
ω = L₁/(I₁ + I₂)
ω = L₁/(1/2MR² + mR²)
ω = L₁/(1/2M + m)R²
substituting the values of the variables into the equation, we have
ω = L₁/(1/2M + m)R²
ω = + 9 kgm²/s/(1/2 × 5 kg + 0.02 kg)(2 m)²
ω = + 9 kgm²/s/(2.5 kg + 0.02 kg)(4 m²)
ω = + 9 kgm²/s/(2.52 kg)(4 m²)
ω = +9 kgm²/s/10.08 kgm²
ω = + 0.893 rad/s
The angular velocity of the cylinder bullet system is 0.893 rad/s in the clockwise direction-since it is positive.
Answer:
The number of protons in one atom of an element determines the atom's identity, and the number of electrons determines its electrical charge. The atomic number tells you the number of protons in one atom of an element. It also tells you the number of electrons in a neutral atom of that element.
Explanation:
If the observer and the source are getting closer together OR getting farther apart, the observer will hear a sound with a different frequency compared to the sound that's actually coming out of the source.
An Austrian physicist and mathematician named Christian Doppler studied this effect, and he worked out the math that tells how much the frequency will change, depending on how fast the source and observer are moving, and whether they're moving together or apart.
After Doppler worked it out other scientists debated and argued for several years what they wanted to CALL this effect.
Some wanted to call it the "Freaky-Shifty Effect", because when the motion is there, the frequency of the source gets shifted.
Other scientists noticed that if the observer moves back and forth and back and forth, the frequency he hears goes up and down and up and down, and it sounds something like "OOWAH-EEYOO OOWAH-EEYOO", so THEY wanted to call it the "Y-U Effect".
After years of disagreement and debate, the cooler scientists found the best way to displease everyone. They just pointed out that it was Doppler who explained the whole thing and worked out all the math, and it would actually be nice to give him some credit for it. So everybody just cooled off and agreed to call it the <em>Doppler Effect</em> .