# HNC Dynamics help please -- Hoist cable looped over a winding drum

Hi guys im looking for help with some formulas, its for hnc mech eng, the question is as follows a winding drum with moment of inertia 24 kg m2 and a winding radius of 0.6m is used to accelerate a loaded hoist with mass of 850kg at a rate of 0.8ms by means of a cable, frictional resistance can be considered as a torque of 88 Nm
determine
1- the tension required in the cable
2- angular acceleration in rads/sec
3- Accelerating torque in Nm at the winding drum shaft required to accelerate the system
4- The total driving torque in Nm required at the winding drum shaft to produce the required motion of the whole system
I got 1 as 90,185N
2 - 1.33 rads/s
3- 5411Nm
4 is 5531Nm but I am not sure how to derive at this answer
The question then goes on to velocity time diagram like questions and asking for sketches
the hoist covers a distance of 20m accelerating at 0.8ms from rest to a max speed then decelerates at the same rate, i.e for 10m constant acceleration
the part of the question im struggling with is where it asks for the maximum velocity of the hoist, this is 4ms but I am beat for knowing the calculation as I don't have an specific time, Could anyone help me with the formula required to achieve the answer of 4ms?

Many thanks!

## Answers and Replies

berkeman
Mentor
Hi guys im looking for help with some formulas, its for hnc mech eng, the question is as follows a winding drum with moment of inertia 24 kg m2 and a winding radius of 0.6m is used to accelerate a loaded hoist with mass of 850kg at a rate of 0.8ms by means of a cable, frictional resistance can be considered as a torque of 88 Nm
determine
1- the tension required in the cable
2- angular acceleration in rads/sec
3- Accelerating torque in Nm at the winding drum shaft required to accelerate the system
4- The total driving torque in Nm required at the winding drum shaft to produce the required motion of the whole system
I got 1 as 90,185N
2 - 1.33 rads/s
3- 5411Nm
4 is 5531Nm but I am not sure how to derive at this answer
The question then goes on to velocity time diagram like questions and asking for sketches
the hoist covers a distance of 20m accelerating at 0.8ms from rest to a max speed then decelerates at the same rate, i.e for 10m constant acceleration
the part of the question im struggling with is where it asks for the maximum velocity of the hoist, this is 4ms but I am beat for knowing the calculation as I don't have an specific time, Could anyone help me with the formula required to achieve the answer of 4ms?

Many thanks!

Welcome to the PF.

First off, you should be a bit more careful typing out the units. You seem to be using ms as a unit of velocity, but hopefully you mean m/s. Similarly what are the units of linear acceleration? What are the units for angular acceleration?

What is the equation that relates Force, mass and acceleration? What is the equation that relates Torque, Moment of Inertia and Angular Acceleration?

Can you show us your calculations for parts 1, 2 and 3? :-)