Formulate conservation of Mechanical Energy for closed system. A mass 12 kg drop

Question

Formulate conservation of Mechanical Energy for closed system. A mass 12 kg dropped from the height of 12 meters. Find its velocity just before the impact. How much heat is generated after it comes to rest? A person weights 189 kg standing on a perfect ice (zero friction), and firing a rifle in a horizontal direction. The weight of the bullet is 20 g and the exit velocity is 100 m/s. Find the velocity of the person after firing the rifle. A spring with the spring constant k has a natural frequency of 15 Hz. Find the mass attached to the spring. A string is bound at two points with distance between them is 56 cm. The tension in a string is 60 N, and mass of string is 15 g. Find the velocity of the standing wave, its natural frequency. How much heat needed to melt 100 g of ice at 0 C degrees. Find buoyancy force on the steel ball of mass 100 g and density 8.05 g/cm^3. What is normal force acting on the ball on bottom of the cup What is decibel level of the sound of 1 w/cm2 Intensity? Which way the heat will flow between two bodies if their temperature is equal

Explanation / Answer

4)

f=1/2*sqrt(k/m)

2f= sqrt(k/m)

(2f)^2= k/m

m=k/(2f)^2

Plugging given data,

m=k/8873.64

m=1.13*10^-4*k

5)

L=0.56m, T=60N,m=0.015kg

v=sqrt(T/µ)=sqrt(T/(m/L))

v=sqrt[60/(0.015/0.56)]

v= 47.33 m/s

f=v/

f=v/2L

f=47.33/(2*0.56)

f= 42.26 Hz

6)

Q=m*Lf = 0.100*335000 = 3.35*10^4 J

9)

I=10log(I/I0)

I=10*log[(10^4)/(10^-12)]

I=10*log[10^16]

I= 160dB

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