Question

An object of mass M₁ travels in a circular path of radius R on a horizontal table. The object is attached to a string that passes through a hole in the center of the table. An object of mass M₂ is attached to the other end of the string and hangs vertically under the table, which produces a force on M₁. All frictional forces are considered to be negligible. Which quantity or quantities must be measured to determine the tangential speed required to keep the system in equilibrium?

Answer 1

M₁, M₂, R

Step-by-step explanation:

Draw free body diagrams for both masses.

M₁ has three forces: tension force T towards the center, gravity force M₁g downwards, and normal force N upwards.

M₂ has two forces: tension force T upwards and gravity force M₂g downward.

Sum the forces on M₁ in the centripetal direction.

∑F = ma

T = M₁ v² / R

Sum the forces on M₂ in the y direction.

∑F = ma

T − M₂g = 0

T = M₂g

Substitute:

M₁ v² / R = M₂g

Solve for v:

v² = (M₂ / M₁) g R

v = √((M₂ / M₁) g R)

Therefore, to calculate the velocity, both masses need to be known, as well as the radius of circular path.