Please help!! The amount a string stretches varies linearly with the mass applied to the spring, as can be seen in the video. In the video, with no additional mass, the hanger was 30.6 cm off the ground. With 150 grams of additional mass, the hanger was 16.2 cm off the ground.

A wooden block stretched the spring so the hanger was 24.5 cm off the ground. Determine the mass of the wooden block, to at least 1 decimal place.

Question

12-09-2017
Mathematics

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Please help!! The amount a string stretches varies linearly with the mass applied to the spring, as can be seen in the video. In the video, with no additional mass, the hanger was 30.6 cm off the ground. With 150 grams of additional mass, the hanger was 16.2 cm off the ground.

A wooden block stretched the spring so the hanger was 24.5 cm off the ground. Determine the mass of the wooden block, to at least 1 decimal place.

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W0lf93 W0lf93 · Answer 1 · 2017-09-25T19:58:24+02:00

63.54 grams First determine by how much the spring stretches for a given mass using deflection for 0 grams as the starting point. 0 g = 30.6 cm 150 g = 16.2 cm X g = 24.5 cm Normalized 0 g = 30.6 - 30.6 = 0 cm 150 g = 30.6 - 16.2 = 14.4 cm X g = 30.6 - 24.5 = 6.1 cm Now the ratio between the distances will be equal to the ratio between the masses. So the expression is 6.1/14.4 = X/150 Solve for X by first multiplying both sides by 150 150*6.1/14.4 = X 915/14.4 = X 63.54 = X So the unknown mass of the wooden block is about 63.54 grams.