Calculate Mass of Cylinder Given Tension & Distance

[doub]

Homework Statement

A light string is wrapped around a solid cylinder and a 300 g mass hangs from the free end of the string, as shown. When released, the mass falls a distance 54 cm in 3.0 s. Calculate the mass of the cylinder?

Homework Equations

not sure

The Attempt at a Solution

I have gotten as far as to determine the Tension on the string of -2.9N. Without known the radius of the cylinder I feel that the mass cannot be determined.

Granted these are study question but if the final is going to be like this...yikes

 

[tiny-tim]

hi doub!

A light string is wrapped around a solid cylinder and a 300 g mass hangs from the free end of the string, as shown. When released, the mass falls a distance 54 cm in 3.0 s. Calculate the mass of the cylinder?
…
Without known the radius of the cylinder I feel that the mass cannot be determined.

the motion depends on what i call the rolling mass of the cylinder, I/r², which is always half the actual mass!

carry on … you should find that the radius cancels out ​

 

[doub]

The best I can get is

$\alpha$ = (T₁ + T₂)/I

= (Fr - Tr)/1/2 mr²

= (mra -(ma+mg)r)/ 1/2 mr²

don't see how the radiii cancel each other though

 

[tiny-tim]

$\alpha$ = (T₁ + T₂)/I

= (Fr - Tr)/1/2 mr²

= (mra -(ma+mg)r)/ 1/2 mr²

sorry, i don't understand any of this

you should have an F = ma equation and a τ = Iα equation

 

[Nickie]

I would approach this problem by first defining the variables and equations needed to solve for the mass of the cylinder. The equation for tension can be used to determine the force acting on the cylinder, and the equation for acceleration can be used to determine the acceleration of the mass. Once these values are known, the equation for torque can be used to solve for the mass of the cylinder.

The equation for tension is T = mg, where T is the tension, m is the mass of the hanging object, and g is the acceleration due to gravity. In this case, we know that T = -2.9N and m = 0.3 kg. Therefore, we can solve for g, which is equal to -9.8 m/s^2.

The equation for acceleration is a = Δv/Δt, where a is the acceleration, Δv is the change in velocity, and Δt is the change in time. In this case, we know that Δv = 0.54 m/s (since the distance is 54 cm and the time is 3.0 s). Therefore, we can solve for a, which is equal to 0.18 m/s^2.

The equation for torque is τ = Fr, where τ is the torque, F is the force acting on the cylinder (in this case, the tension), and r is the radius of the cylinder. We know that τ = ma = 0.3 kg * 0.18 m/s^2 = 0.054 Nm. We also know that F = -2.9N. Therefore, we can solve for r, which is equal to 0.0186 m.

Now that we know the radius of the cylinder, we can use the formula for the volume of a cylinder (V = πr^2h) to determine the mass of the cylinder. The height (h) is not given in the problem, so we cannot solve for the exact mass of the cylinder. However, we can determine the range of possible masses by assuming different values for the height.

In conclusion, the mass of the cylinder cannot be determined without knowing the height or length of the cylinder. However, we can determine the range of possible masses by using the information we have and assuming different values for the height.