Explanation:
(a) Draw a free body diagram of the cylinder at the top of the loop. At the minimum speed, the normal force is 0, so the only force is weight pulling down.
Sum of forces in the centripetal direction:
∑F = ma
mg = mv²/RL
v = √(g RL)
(b) Energy is conserved.
EE = KE + RE + PE
½ kd² = ½ mv² + ½ Iω² + mgh
kd² = mv² + Iω² + 2mgh
kd² = mv² + (m RC²) ω² + 2mg (2 RL)
kd² = mv² + m RC²ω² + 4mg RL
kd² = mv² + mv² + 4mg RL
kd² = 2mv² + 4mg RL
kd² = 2m (v² + 2g RL)
d² = 2m (v² + 2g RL) / k
d = √[2m (v² + 2g RL) / k]
We use the formula,
.
Here, v is velocity and its value given 26 mi/h ( in m/s, 
) and d is distance and its value is given 80 m.
Substituting these values in above formula we get,
Thus, the time delay between green lights on successive blocks to keep the traffic moving continuously is 6.88 s
The eight planets of the Solar System arranged in order from the sun:
Mercury: 46 million km / 29 million miles (.307 AU)
Venus: 107 million km / 66 million miles (.718 AU)
Earth: 147 million km / 91 million miles (.98 AU)
Mars: 205 million km / 127 million miles (1.38 AU)
Jupiter: 741 million km /460 million miles (4.95 AU)
Saturn: 1.35 billion km / 839 million miles (9.05 AU)
Uranus: 2.75 billion km / 1.71 billion miles (18.4 AU)
Neptune: 4.45 billion km / 2.77 billion miles (29.8 AU)
Astronomers often use a term called astronomical unit (AU) to represent the distance from the Earth to the Sun.
+ Pluto (Dwarf Planet): 4.44 billion km / 2.76 billion miles (29.7 AU)
10.67m/s²
32N
Explanation:
Given parameters:
Mass of the body = 3kg
velocity of the mass = 4m/s
radius of circle = 0.75m
Unknown:
centripetal acceleration = ?
centripetal force = ?
Solution:
The centripetal force is the force that keeps a radial body in its circular motion. It is directed inward:
Centripetal acceleration = 
v is the velocity of the body
r is the radius of the circle
putting in the parameters:
Centripetal acceleration = 
Centripetal acceleration = 10.67m/s²
Centripetal force = m
m is the mass
Centripetal force = mass x centripetal acceleration
= 3 x 10.67
= 32N
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static electricity and friction
