Find the tensions between the blocks on the 30 degree frictionless inclined plan

Question

Find the tensions between the blocks on the 30 degree frictionless inclined plane. Assuming no friction, find the acceleration and the tension. A 50N horizontal force pushes a 1kg and a 3kg block up a frictionless 37 degree inclined plane. Assuming there is no friction, find the contact forces. When the cart accelerate the pendulum swings to angle theta. Find the acceleration in terms of the angle. A block mass m sits on a cart with coefficient of friction mu_s. What is the maximum acceleration that the cart can have without the block slipping.

Explanation / Answer

24) Let the rightmost tension be T1, middle be T2 and left be T3.

let the system accelerates with a,

15g - T3 = 15a

T3-T2 - 3g*sin 30 degree  = 3a

T2-T1 - 2g*sin 30 degree = 2a

T1 - g*sin 30 degree = a

adding all four equations

15 g - (3+2+1)g sin 30 degree = (15+3+2+1)a

12 g = 21a

a = 12g/21 = 4g/7 = 4*9.8/7 = 5.6 m/s^2

T1 = a +0.5g = 5.6+4.9 = 10.5 N

T2 = T1+2a+g = 10.5+2*5.6+9.8 = 31.5 N

T3 = 15 g - 15a = 15*(9.8-5.6) = 63 N

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