Question

Atwood's machine consists of two blocks connected by a string suspended over a pulley as illustrated in Fig. 2. Typ ically the two blocks are released from rest. Newton's laws can be used to predict their subsequent acceleration, which can also be determined by measuring the speeds of the blocks as time passes. The aim of this experiment is to verify the accelerations as predicted by Newton's second law R1 Figure 2: Atwood's machine. Block 1 is on the left, block 2 is on the right 1 T heory and experimental design a) Suppose that the string cannot stretch. How is the velocity of block 1 at one instant related to that of block 2 at the same instant? How is the acceleration of block 1 related to that of block 2? b) Assume that m2 > mi and consider block 1 in Fig. 2. Is the y-component of its acceleration positive, negative or zero? Is the y-component of the acceleration of block 2 positive, negative or zero? Denote the magnitude of the acceleration of each block by a c) Express the y-component of each block's acceleration in terms of a d) Draw a free body diagram for each block e) Apply Newton's second law separately to each block. This should give two equations with two unknowns: a and the tension in the string. Combine these to determine an expression for the magnitude of the acceleration, i.e α = formila where the only allowed symbols are m1, m2 and g f) What does your expression predict for the acceleration when the blocks have the same mass? Does your prediction appear to be correct? If it predicts this correctly then have the instructor check your expression for the acceleration The sensor records the spood of block 1 versus tine. How can the acceleration the this block be determined from this data?

Answer 1