3/20 The winch takes in cable at the rate of 200 mm/s, and this rate is momentarily increasing at 500 mm/s each second. Determine the tensions in the three cables. Neglect the weights of the pulleys.

The tension in the cable = 993.5 N

The tension in the cable  496.75  N

The tension in the cable = 248.375 N

Explanation:

The diagram attached below depicts the full understanding of what the question is all about.

Now, obtaining the length of cable 1 from the diagram; we have:

where;

= distance from the fixed point to point B

= distance from the fixed point to pulley A

From the cable 2 as well.we obtain its length

where :

distance from the fixed point to the weight attached to the pulley

Let differentiate equation (1) in order to deduce a relation between the velocities of A and B with respect to time ;

Since is constant ; Then:

where;

velocity at point B

= velocity at pulley A

Let differentiate equation (2) as well in order to deduce a relation between the velocities of W and A with respect to time :

Since is constant ; Then:

where;

the velocity of the weight

Let differentiate equation (3) in order to deduce a relation between accelerations A and B with respect to time  

where;

= acceleration at A

acceleration at B

Replacing 0.5 m/s ² for in equation (5); then

Let differentiate equation (4) in order to deduce a relation between W and A with respect to time

where;

= acceleration of weight W

Replacing - 0.25 m/s² for

From the second diagram, if we consider the equilibrium of forces acting on the cylinder in y-direction; we have:

where;

m= mass of the cylinder = 100 kg

= tension in the string = ???

g = acceleration due to gravity = 9.81 m/s²

= acceleration of the cylinder =

Plugging all values into above equation; we have

(100 × 9.81) - = 100(-0.125)

= 993.5 N

∴ The tension in the cable = 993.5 N

From the third diagram, if we consider the equilibrium of forces acting on the cylinder in y-direction on the pulley ; we have:

where ;

= tension in cable 2

Replacing 993.5 N for ; we have

∴ The tension in the cable

From the fourth  diagram, if we consider the equilibrium of forces acting on the cylinder in y-direction on the pulley A ; we have

where;

= tension in  cable 1

Replacing 496.75 N for in the above equation; we have:

= 248.375 N

∴ The tension in the cable = 248.375 N

it about 600 mph from what i calculated

this is a good question! i'll do some research and come back when i have the answer!