Could you please help me with the following. If you could show your work it woul

Question

Could you please help me with the following. If you could show your work it would be appreciated, I want to know how to solve this type of problem. Thank you for your help

Consider a 250-gram cart loaded with additional 250 grams (for a total mass of 500 grams) sitting on a frictionless track and having zero initial velocity. A string passed over a pulley attached to one end of the track connects the cart with a vertical 50-gram mass hanger. Your objective is to apply the Newton’s Second Law of motion in order to calculate to what angle (let’s call it “critical”) should the track be tilted (made into an incline) to prevent the cart from moving in either direction

Explanation / Answer

Here ,

let the angle be theta

for the crictial angle , so that the cart just starts to move

Tension in wire , T = 0.050 * 9.8

net force on cart = 0

0.5 * 9.8 * sin(theta) - T = 0

0.5 * 9.8 * sin(theta) - 0.050 * 9.8 = 0

sin(theta) = 0.1

theta = 5.74 degree

the critical angle is 5.74 degree

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