Final answer:
The velocity of sliding when the contact is at the tip of the teeth of Gear 2 is 100 m/s. So, none of the given options are correct.
Step-by-step explanation:
The velocity of sliding when the contact between the teeth occurs at the tip of Gear 2 can be calculated using the formula:
Velocity of sliding = (r₁ + r₂) * (ω₁ - ω₂)
where r₁ is the radius of Gear 1, r₂ is the radius of Gear 2, ω₁ is the angular velocity of Gear 1, and ω₂ is the angular velocity of Gear 2.
In this case, r₁ is the distance from the center of Gear 1 to the point of contact, and r₂ is the distance from the center of Gear 2 to the tip of its teeth.
Given that Gear 1 has 20 teeth and Gear 2 has 30 teeth, we can calculate the distances as follows
r₁ = (2 * π * 20) / (2 * π) = 20
r2 = (2 * π * 30) / (2 * π) = 30
Substituting the given values into the formula:
Velocity of sliding = (20 + 30) * (10 - 6) = 100 m/s
Therefore, the velocity of sliding when the contact is at the tip of the teeth of Gear 2 is 100 m/s.
None of the given options are correct.
Question: In a gear system, Gear 1 with a certain number of teeth is driving Gear 2, which also has a specific number of teeth. If the point of contact between the teeth occurs at the tip of Gear 2, what is the velocity of sliding when the contact is at the tip of the teeth of gear 2?
Gear 1 has 20 teeth (N 1 =20).
Gear 2 has 30 teeth (N 2 =30).
The angular velocity of Gear 1 is 10 radians per second (ω 1 =10rad/s).
The angular velocity of Gear 2 is 6 radians per second (ω 2 =6rad/s).
a) 15.28 m/s
b) 20.42 m/s
c) 25.12 m/s
d) 30.45 m/s