# accelerating painter

#### uxinox

Hi guys,

A painter is hanging in a cage on the outside of a building. When the painter, who weighs 1000N pulls on the rope he exerts a force on the floor of the cage of 450N. The cage weighs 250N. Find the acceleration.

The tension in the rope balances the man and cage and the system is in equilibrium. The cage only moves when the force of 450 N is applied.

So, I reckon

450 = ma

the force has to overcome the weight of man and cage so

F = 1000 + 250 = mg

so, m = 1250/10 = 125 kg

therefore

450 = 125a

$a = 3.6 m/s^2$

My book has $2 m/s^2$ can anyone explain this?

#### Woody

He weighs 1000N
he exerts a force of 450N on the floor
The other 550N must go somewhere (the rope)

The total downward force is (450+250)N

The tension in the rope balances the man and cage and the system is in equilibrium
do you mean?
The tension in the rope balances the man and cage when the system is in equilibrium.

1 person

#### uxinox

Hi Woody,

I thought the man and cage would be stationary while he was painting and if he wanted to go up he pulled the rope.
I see what you mean. If he does so, the 450N is deducted from his body weight so we have
a net force of 700 N

so, can we say
700 = ma

m is the mass of the system i.e. man and cage = (1000 + 250)/g = 125 kg

#### oz93666

This has had me puzzled for quite some time....are you sure you've given all the question???

A painter is hanging in a cage on the outside of a building. When the painter, who weighs 1000N pulls on the rope he exerts a force on the floor of the cage of 450N. The cage weighs 250N. Find the acceleration.

he and his cage are hanging on a rope ....no mention of any pulleys or counterweights..we must assume the other end of the rope is tied to the building...

Why should pulling on the rope accelerate anything anywhere???

Even if the rope was attached to pulleys and counterweights the tension being transmitted up the rope will not be effected by the man pulling on his part of the rope.

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1 person

#### uxinox

There is a pulley attached to the building. A rope over one side of the pulley attaches to the top of the cage. The man has the other end of the rope in his hand. He is sitting on the floor of the cage.

I would send you a sketch, but I can't see how to do it as an attachment. Sorry if I have not made it clear.

#### oz93666

The man pulls the rope with force T which is the force accelerating the cage and him

T= 125a ................. his force on the floor before pull is 1000 during pull it's 450

so force on man is T pulling him up ...450 pushing him up ....his weight 100g pushing him down and this results in him accelerating up

So T + 450 - 1000 = 100a

This gives a silly answer , perhaps his force on the floor is 1450 during pull ....

T + 1450 -1000 = -100a ............... -125a -100a = 450 ... a = 2m/sec/sec

The question should read " when pulling the rope the painter exerts an ADDITIONAL force of 450N on the floor"

2 people

#### uxinox

Thanks oz. At least I see the issues now. It is an old physics book. From when I was at school!