the figure at the right shows two carts, connected by a lightweight string. anot
ID: 582254 • Letter: T
Question
the figure at the right shows two carts, connected by a lightweight string. another string runs over a massless, frictionless pulley to a hanging mass.
for 1 and 2 cart A is held stationary by a hand.
1) compare the tension in string 1 to the tension in string 2. be explicit about which of newton's laws applies. explain and use a free body diagram.
2) Find an expression for the tension.also use a free body diagram .
Now cart A is released and the system accelerates to the right. the string cannot stretch.
3)compare the acceleration of cart A and cart B explain and use a free body diagram.
4) compare the tension in string 1 and 2 as the system accelerates explain and use a free body diagram when explaining
5) compare the tension in string 2 as the system accelerates to its value when the system is held stationary use a free body diagram when explaining
6)compare the tensions in string 1 as the system accelerates to its value when the system is held stationary explain and use a free body diagram when explaining.
Explanation / Answer
1) Since A is held stationary so B is not able to move as well, but net force on B must be zero hence the tenstion T1 must be equal to the tension T2.
In free body diagram of B, there will be two vertical forces, one is normal upward and another is force due to gravity.In horizontal direction there are two forces T1 and T2 which are equal and opposite.
2) Since rope is massless and there is no motion possible, the net force on hanging mass will be zero hence T2 = mg which in turn will equal to T1.
T1 = T2 = mg
3) All three are conneted to a string which can't be stretched further hence all will be having same acceleration.
4) Now block B is having an acceleration towards the right hence there must be net force working on B in the right direction. So T2-T1>0 or T2>T1.
5) Looking at hanging block, now this block is having acceleration to the tension will be less than mg which was equal in the case of part 2. So the tension T2 is reduced.
6) When system was stationary T1 was mg but now since T1<T2<mg, the tension T1 is reduced now.
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