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]
Kinetic Energy = 1/2 * m * v²
1/2 * 30 * 20²
1/2 * 30 * 400
12000/2
6000 J.
Coke has more fizz than Pepsi, because Coke has more carbonation in it. Pepsi contains more sugar (2 more tablespoons) than Coke, so it tastes slightly sweeter to many people.
D. Budgeting time, avoiding stress, and prioritizing.
