Two students wish to determine the value of g, the acceleration due to gravity at Earth’s surface. The students have a collection of blocks of different masses, a string of negligible mass, a pulley of negligible mass, and a device for measuring acceleration. The students attach two of the blocks to the ends of the string and pass the string over the pulley so the blocks hang vertically on either side. The blocks are then released from rest, and their acceleration is measured. The students’ data for one trial are shown below, with m1 and m2 equal to the masses of the blocks. Considering the gravitational forces acting on the blocks, do the data provide a reasonable determination of the value of g, and what is a possible justification for why or why not?

D) No, because the calculated value of g is too small, possibly due to an additional force exerted on the block-string system.

Explanation:

In order to find the value of g, we have to write the equation of the forces on the two blocks.

Since m2 is heavier than m1, this means that m2 will accelerate downward while m1 will accelerated upward, because of the tension in the rope.

For m2, we have:

(2)

where

is the weight of block m2, with

is the mass

is the acceleration due to gravity

T is the tension in the rope

is the acceleration measured

For m1, we have

(1)

where

is the weight of block m1, with

mass of m1

Re-writing T from (1) and replacing it into (2), we find

However, we know that the true value of g is : so the correct answer is

D) No, because the calculated value of g is too small, possibly due to an additional force exerted on the block-string system.

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