Solving Two Worlds Spinning: Calculating Tension (T) in String

[soupastupid]

Homework Statement

There are two balls with masses m_a and m_b connected by a string. m_b is moving at a velocity v upwards (perpendicular to the string) and it asks for the Tension (T) in the string.

Homework Equations

a=(v^2)/R
delta Energy of system = 0

T = m((u^2)/r)
u is linear speed of rotational motion
r = radius of motion

The Attempt at a Solution

The initial kinetic energy of m_b = .5(m_b)v^2

and that's as far as I got.
Is mass B moving?

how do I start this problem?

 

[Doc Al]

Homework Equations

a=(v^2)/R

That will come in handy.

The initial kinetic energy of m_b = .5(m_b)v^2

Why did you calculate the energy?

and that's as far as I got.
Is mass B moving?

Mass B's velocity is described in the problem statement.

Hint: Viewed from the inertial lab frame, mass B is in pure rotation about mass A (at the instant shown). Apply Newton's 2nd law.

 

[thomate1]

I would first clarify any missing information or assumptions in the problem statement. For example, it is not clear if the two balls are connected by a rigid or flexible string, and if there are any external forces acting on the system. Additionally, it is important to define the direction of motion and the reference frame for the problem.

To solve this problem, we can use the principle of conservation of energy, which states that the total energy of a closed system remains constant. In this case, the system consists of the two balls and the string.

We can start by considering the initial and final states of the system. In the initial state, the two balls are connected by a string and m_b is moving with a velocity v. In the final state, the two balls are still connected by the string, but m_b may have a different velocity and the string may experience a tension force.

Next, we can apply the equation for kinetic energy, K = 1/2mv^2, to the initial and final states. We know that the initial kinetic energy is given by .5(m_b)v^2, but we need to calculate the final kinetic energy.

To do this, we can use the equation for linear speed, v = ωr, where ω is the angular velocity and r is the radius of motion. We can also use the equation for centripetal acceleration, a = v^2/r, to relate the linear and angular velocities.

By setting the initial and final kinetic energies equal to each other, we can solve for the tension in the string, T. This will give us an equation for T in terms of the masses, velocities, and radius of motion.

It is also important to consider any external forces acting on the system, such as gravity or friction. These forces may affect the final velocity and therefore the calculated tension in the string.

In summary, to solve this problem we need to clarify any missing information, define the reference frame and direction of motion, apply the principle of conservation of energy, and consider any external forces on the system.