- #1

swotty

- 4

- 1

## Homework Statement

An object of mass 1000 kg is lifted by means of a steel lifting cable being wound round a drum of diameter 2.5m mounted on a horizontal shaft. The drum and shaft have a mass of 1000 kg and a radius of gyration of 1.0 m. What is the torque required to give the object an upward acceleration of 0.75 m/s^2

## Homework Equations

Tension in cable ##Fc=mg + ma##

Moment of inertia ##I=mk^2##

Torque ##T=I\alpha=Fr##

Linear acceleration ##a=r\alpha##

## The Attempt at a Solution

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My problem is I don't get the answer given in the textbook. Which is 11.2 kNm. I always assume at first that I have missed something. But I've tried various tacks and still do not get this answer. Am I missing something?

Here is my calculations:

Tension in cable due to mass of object and acceleration upwards:

$$F_{c}=1000\times9.81 + 1000\times0.75$$

$$=10560N$$

Torque on rim of drum to create tension:

$$T_1=Fc\times r $$##(r=radius of drum)##

$$T_1=10560\times 1.25$$

$$=13.2\times10^3 Nm$$

Torque to accelerate drum:

$$T_2=I\times\alpha$$

$$I=1000\times 1^2=1000 kg m^2$$

acceleration Angular

$$\alpha = a/r$$

$$ \alpha =0.75/1.25$$

$$\alpha = 0.6 rad/s^2$$

$$T_2=1000\times0.6$$

$$T_2=600Nm$$

Total Torque to accelerate drum and object:

$$T_n=T_1+T_2$$

$$T_n=13.2\times10^3+600$$

$$T_n=13.8kNm$$