Hello!
a) Assuming this is asking for the minimum speed for the rock to make the full circle, we must find the minimum speed necessary for the rock to continue moving in a circular path when it's at the top of the circle.
At the top of the circle, we have:
- Force of gravity (downward)
*Although the rock is still connected to the string, if the rock is swinging at the minimum speed required, there will be no tension in the string.
Therefore, only the force of gravity produces the net centripetal force:

We can simplify and rearrange the equation to solve for 'v'.

Plugging in values:

b)
Let's do a summation of forces at the bottom of the swing. We have:
- Force due to gravity (downward, -)
- Tension force (upward, +)
The sum of these forces produces a centripetal force, upward (+).

Rearranging for 'T":

Plugging in the appropriate values:

Answer
The same number of particles in a gas spread further apart than in the liquid or solid states.
Explanation:
The same number of particles in a gas spread further apart than in the liquid or solid states. The same mass takes up a bigger volume. This means the gas is less dense. Density also depends on the material.
Answer:
-35 m/s
Explanation:
Momentum is conserved.
Momentum before firing = momentum after firing
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Before the bullet is fired, the bullet and rifle have no velocity, so u₁ and u₂ are 0.
0 = m₁v₁ + m₂v₂
Given m₁ = 0.7 kg, v₁ = 350 m/s, and m₂ = 7 kg:
0 = (0.7 kg) (350 m/s) + (7 kg) v
v = -35 m/s
The rifle recoils at 35 m/s in the opposite direction.