Two hanging objects are attached by strings and pulleys to an cart on a friction

Question

Two hanging objects are attached by strings and pulleys to an cart on a frictionless track as shown below. M1 = 250 g,M2= 200 g and M3 = 400 g. Draw force diagrams for each object on the diagram above and indicate the direction of acceleration beside each object Write down force equations (no numbers!) for each block. (Hint: The tension force exerted on M2 by the string on the right does not equal the tension force exerted on M2 by the string on the left-) Use your equations to find the acceleration of the system. Find the tension force exerted by each string on M2. Find the acceleration of the system if you take the wheels off the cart and the coefficient of friction between the table and the cart(M2) is 0.25. (Assume the mass of the cart stays the same.)

Explanation / Answer

(b) T1 -M1g = M1a

M3g -T3= M3a

T3- T1 = M2a

(c)M3 -M1=(a/g)(M1+M2+M3)

-->a=(M3 -M1)g/(M1+M2+M3)

(d)T1 =M1(a+g)

T3=M3(g-a)

(e) M3g-M2g-M1g =(M1+M2+M3)a

-->a = (M3 -M2- M1)g/(M1+M2+M3)

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