Increased acceleration in a pully system

[coneheadceo]

Homework Statement

A window washer pulls themself upward using a bucket/single pulley system. Their weight with the bucket is 65 Kg.
a) How hard must she pull doward to raise herself slowly at a constant speed?
b) If they increase the force by 15% what will her accelertion be?

Homework Equations

2Ft - mg = ma

a = (Mb - Mp)/(Mb+Mp) ... I think

The Attempt at a Solution

a) I've got no problem...

to get constant speed accel = 0 so...

2Ft - mg = 0
2Ft = mg
Ft = mg/2 -> (65)(9.8)/2 = 320 N

b) This is where I think I have the wrong equation to attempt this as
(320)(0.15)= 48, so ... [(368-320)/(368+320)](9.8)= 0.68 m/s^2

answer in the book is 1.5 m/s^2 so need something else but don't know what to use.

 

[ehild]

Homework Statement

A window washer pulls themself upward using a bucket/single pulley system. Their weight with the bucket is 65 Kg.
a) How hard must she pull doward to raise herself slowly at a constant speed?
b) If they increase the force by 15% what will her accelertion be?

Homework Equations

2Ft - mg = ma

a = (Mb - Mp)/(Mb+Mp) ... I think

The Attempt at a Solution

a) I've got no problem...

to get constant speed accel = 0 so...

2Ft - mg = 0
2Ft = mg
Ft = mg/2 -> (65)(9.8)/2 = 320 N

b) This is where I think I have the wrong equation to attempt this as
(320)(0.15)= 48, so ... [(368-320)/(368+320)](9.8)= 0.68 m/s^2

answer in the book is 1.5 m/s^2 so need something else but don't know what to use.

The equation in red is irrelevant here. The person exerts F force, and the tension in the chord equals to F_t=F. The person in the bucket is pulled by 2F_t upward, and gravity pulls downward. So the equation you wrote 2Ft - mg = ma is correct.

The other equation refers to the case of a pulley with two masses.

ehild

 

[azizlwl]

Your new upward force is 2(320+48)

 

[coneheadceo]

So am I literally taking (9.8 m/s^2)(0.15)= 1.47 m/s^2 to get the acceleration?

 

[ehild]

So am I literally taking (9.8 m/s^2)(0.15)= 1.47 m/s^2 to get the acceleration?

Yes.

ehild