Answer:
K.E = 0.0075 J
Explanation:
Given data:
Mass of the ball = 1.5 kg
radius, r = 50 cm = 0.5 m
Angular speed, ω = 12 rev/min = (12/60) rev/sec = 0.2 rev/sec
Now,
the kinetic energy is given as:
K.E = 
where,
I is the moment of inertia = mr²
on substituting the values, we get
or
K.E = 0.0075 J
Answer:
a) t=24s
b) number of oscillations= 11
Explanation:
In case of a damped simple harmonic oscillator the equation of motion is
m(d²x/dt²)+b(dx/dt)+kx=0
Therefore on solving the above differential equation we get,
x(t)=A₀
where A(t)=A₀
A₀ is the amplitude at t=0 and
is the angular frequency of damped SHM, which is given by,
Now coming to the problem,
Given: m=1.2 kg
k=9.8 N/m
b=210 g/s= 0.21 kg/s
A₀=13 cm
a) A(t)=A₀/8
⇒A₀ =A₀/8
⇒
applying logarithm on both sides
⇒
⇒
substituting the values
b)
, where 
is time period of damped SHM
⇒
let 
be number of oscillations made
then, 
⇒
Radiation: Getting sunburnt on a beach.
- The sun’s radiation (no direct contact) is what causes the skin to burn.
Radiation: Microwave cooking food
- Microwaves use radiation to heat the food inside of it; between radio waves and infrared radiation on the electromagnetic spectrum
Conduction: Touching a hot car seat in the summer
- Conduction is the transfer of heat by direct contact (hand to seat).
Conduction: Burning yourself with a curling iron (Similar to above; direct contact).
Convection: An ocean breeze
- Convection near coastlines cause the transfer of energy; water warms and cools slower than land.
Conduction: Sliding down a hot metal slide in august
- You are in direct contact with the slide, which is hot due to the temperature.
Convection: Water in a boiling pot of macaroni
- The water, a liquid, is being heated by molecular motion.
Convection: Currents deep within the earth that cause tectonic plates to move
- Convection currents drive the movement of tectonic plates in the mantle, which is fluid/molten. The currents circulate under the asthenosphere.
Answer:
Calculate using the formula
Explanation:
velocity= displacement (m)/time(s)
1 mile =1.6km
1km=1000m
