Two objects are connected by a light string that passes over a frictionless pulley, and two objects are on either side of the string. There is a hanging object off the vertical side of the incline weighing 10.0 kg. The 3.50 kg object lies on a smooth incline of angle 37.0°. Find the tension of the 3.50 kg object.

Question

Would the answer be mg cos 40, since the weight of the object determines the force, with the incline affecting it? Thank you

Answer 1

No, the weight PLUS the acceleration determines the force pullng.

pulling force= 10g
massbeingaccelerated( 10+3.50)kg
retarding force: 3.5gSin40

10g-3.5gSin40=(10+3.5)acceleration
solve for acceleration.

Now tension pulling: two ways.
Tension holding the 10kg weight..
10g-10*acceleration= tension
Tension pulling the 3.5kg..
Tension= 3.5*acceleration+3.5*g*Sin40

Yes, the two tensions will be equal. You probably ought to prove that to yourself.