#### Leilei

59. A pulley is essentially weightless and frictionless. If m1 weighs 100N and the m2 weighs 300 N, and someone holds on to m1 so that the system is motionless, what is the tension in the rope and the acceleration of m1? How much force must the eprson exert and in what direction?

There is a drawing of the pulley system attached to this post.

Anyway, this is what I did:

Ft = tension

m1g = 100 N

m2g = 300 N

so with some calculations, with g = 9.81 m/s^2, m1 = 10.2 kg and m2 = 30.6 kg

Then I said m1a = m1g - Ft --> m1a = m1g - Ft

And m2a = Ft - m2g --> Ft - m2g

Then I said Ft = m1g - m1a and Ft = m2a + m2g

Then m1g - m1a = m2a + m2g

So plugging everything in and solving for a:

(100 N) - (10.2 kg)a = (30.6 kg)a + 300 N

a = -4.90 m/s^2

OK I wasn't sure if I was suppose to calculate with the negative sign, but anyway... trying to find Ft:

Ft = m1g - m1a

Ft = 100 N - (10.2 kg)(-4.90kg)

Ft = 150 N

Did I do this correctly? Because the answer in the back of my Physics book says the answer is suppose to 300 N, but I can't figure out how they got this answer. Any help would be appreciated.