Consider the motion of the rock in the figure below. What is the minimum speed the rock can have without the string becoming "slack"? (The rock is traveling in vertical circle. Assume that m = 1.6 kg and r = 0.48 m.)
What is the minimum speed the rock can have without the string becoming "slack"? (The rock is traveling in vertical circle. Assume that m = 1.6 kg and r = 0.48 m.)
At the top,
mv^2/r=mg
v= sqrt(rg)
2.2m/s
Could someone explain how to do this?
the equation is A(c)= v^(2)/r
solve for v, which is v=[A(c) x r]^(1/2)
A(c)=9.81, r=radius=.48m, mass is irrelevant.
solve for v: v= [9.81 x .48]^(1/2)
v= [4.7088]^(1/2)
v= 2.169
Mars has two moons, Phobos and Deimos. It is known that the larger moon, Phobos, has an orbital radius of 9.4 106 m and a mass of 1.1 1016 kg. Find its orbital period.
To find the minimum speed the rock can have without the string becoming "slack," we need to understand the forces acting on the rock when it is at the topmost point of the vertical circle.
When the rock is at the top, there are two main forces acting on it: the tension in the string and the weight of the rock. The tension in the string is responsible for keeping the rock moving in a circle, while the weight of the rock is responsible for trying to pull it down.
At the topmost point, the tension in the string should be equal to the weight of the rock to prevent the string from becoming slack. Therefore, we can equate these two forces:
Tension in the string = Weight of the rock
The weight of the rock can be calculated using the formula:
Weight = mass × acceleration due to gravity
Now, let's plug in the given values:
mass (m) = 1.6 kg
radius (r) = 0.48 m
The acceleration due to gravity can be approximated as 9.8 m/s².
Weight = 1.6 kg × 9.8 m/s²
Simplifying the equation:
Weight ≈ 15.68 N
Now, since the tension in the string at the topmost point should be equal to the weight, we have:
Tension in the string = 15.68 N
The tension in the string can be related to the speed of the rock using the centripetal force equation:
Tension in the string = (mass × velocity²) / radius
We rearrange this equation to solve for velocity:
velocity² = (Tension in the string × radius) / mass
Plugging in the values we already know:
velocity² = (15.68 N × 0.48 m) / 1.6 kg
Simplifying the equation:
velocity² ≈ 4.704 m²/s²
Finally, taking the square root of both sides:
velocity ≈ 2.17 m/s
Therefore, the minimum speed the rock can have without the string becoming "slack" is approximately 2.17 m/s.