Question

The spring constant of an automotive suspension spring increases with increasing load due to a spring coil that is widest at the bottom, smoothly tapering to a smaller diameter near the top. The result is a softer ride on normal road surfaces from the narrower coils, but the car does not bottom out on bumps because when the upper coils collapse, they leave the stiffer coils near the bottom to absorb the load. For a tapered spiral spring that compresses 12.9 $\mathrm{cm}$ with a $1000-\mathrm{N}$ load and 31.5 $\mathrm{cm}$ with a $5000-\mathrm{N}$ load, (a) evaluate the constants $a$ and $b$ in the empirical equation $F=a x^{b}$ and $(b)$ find the work needed to compress the spring $25.0 \mathrm{cm} .$

Name: the spring constant of an automotive suspension spring increases with increasing load due to a spring coil that is widest at the bottom smoothly tapering to a smaller diameter near the top the result
Uploaded: 2021-09-12T09:43:01-08:00
Duration: 6 min 11 s
Channel: Pritesh Ranjan
Description: the spring constant of an automotive suspension spring increases with increasing load due to a spring coil that is widest at the bottom smoothly tapering to a smaller diameter near the top the result

          The spring constant of an automotive suspension spring increases with increasing load due to a spring coil that is widest at the bottom, smoothly tapering to a smaller diameter near the top. The result is a softer ride on normal road surfaces from the narrower coils, but the car does not bottom out on bumps because when the upper coils collapse, they leave the stiffer coils near the bottom to absorb
the load. For a tapered spiral spring that compresses 12.9 $\mathrm{cm}$ with a $1000-\mathrm{N}$ load and 31.5 $\mathrm{cm}$ with a $5000-\mathrm{N}$ load, (a) evaluate the constants $a$ and $b$ in the empirical equation $F=a x^{b}$ and $(b)$ find the work needed to compress the spring $25.0 \mathrm{cm} .$

Added by Diane A.

Physics for Scientists and Engineers

Raymond A. Serway, John W. Jewett 6th Edition

Chapter 7

Instant Answer

Solved by Expert Pritesh Ranjan

09/12/2021

Step 1

From the first data point (1000 N, 12.9 cm), we have: $1000 = a(0.129)^b$ From the second data point (5000 N, 31.5 cm), we have: $5000 = a(0.315)^b$ Show more…

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The spring constant of an automotive suspension spring increases with increasing load due to a spring coil that is widest at the bottom, smoothly tapering to a smaller diameter near the top. The result is a softer ride on normal road surfaces from the narrower coils, but the car does not bottom out on bumps because when the upper coils collapse, they leave the stiffer coils near the bottom to absorb the load. For a tapered spiral spring that compresses 12.9 $\mathrm{cm}$ with a $1000-\mathrm{N}$ load and 31.5 $\mathrm{cm}$ with a $5000-\mathrm{N}$ load, (a) evaluate the constants $a$ and $b$ in the empirical equation $F=a x^{b}$ and $(b)$ find the work needed to compress the spring $25.0 \mathrm{cm} .$