(a) Explanation The force exerted by the spring can be empirically found by the formula given in question. Write the expression for empirical formula of force. F = a x b (I) Here, a is constant, b is also constant and x is compression of the spring. Case (i): Substitute 12.9 cm for x and 1000 N for F in equation (I). 1000 N = a ( ( 12.9 cm ) ( 1 m 100 cm ) ) b Rearrange above equation for a . a = 1000 N ( 0.129 m ) b (II) Case (ii): Substitute 31.5 cm for x and 5000 N for F in equation (I). 5000 N = a ( ( 31.5 cm ) ( 1 m 100 cm ) ) b (III) Substitute 1000 N ( 0 (b) To determine The work needed to compress the spring.

Physics for Scientists and Engineers With Modern Physics

9th Edition

ISBN: 9781133953982

Author: SERWAY, Raymond A./

Publisher: Cengage Learning

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Chapter 7, Problem 62AP

(a)

To determine

The constants a and b in the empirical equation for F.

.

(b)

To determine

The work needed to compress the spring.

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Chapter 7, Problem 61AP

Chapter 7, Problem 63AP

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Truck suspensions often have "helper springs" that engage at high loads. One such arrangement is a leaf spring with a helper coil spring mounted on the axle, as shown in the figure below. When the main leaf spring is compressed by distance yo, the helper spring engages and then helps to support any additional load. Suppose the leaf spring constant is 4.90 x 105 N/m, the helper spring constant is 3.60 x 105 N/m, and yo = 0.500 m. Truck body Axle (a) What is the compression of the leaf spring for a load of 4.70 x 105 N? 0.87 Your response differs from the correct answer by more than 10%. Double check your calculations. m (b) How much work is done in compressing the springs? 0.855 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. J

Truck suspensions often have "helper springs" that engage at high loads. One such arrangement is a leaf spring with a helper coil spring mounted on the axle, as shown in the figure below. When the main leaf spring is compressed by distance yo, the helper spring engages and then helps to support any additional load. Suppose the leaf spring constant is 4.80 x 10° N/m, the helper spring constant is 3.80 x 10° N/m, and Y. = 0.500 m. Truck body -"Helper" spring Main leaf spring Axle (a) What is the compression of the leaf spring for a load of 5.10 x 10° N? 0 81 (b) How much work is done in compressing the springs? 1 34 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. J Need Help? Read It

Truck suspensions often have "helper springs" that engage at high loads. One such arrangement is a leaf spring with a helper coil spring mounted on the axle, as shown in the figure below. When the main leaf spring is compressed by distance y0, the helper spring engages and then helps to support any additional load. Suppose the leaf spring constant is 5.50 ✕ 105 N/m, the helper spring constant is 3.40 ✕ 105 N/m, and y0 = 0.500 m. A side view of a truck suspension. The truck body is above the wheel. The main leaf spring spans the horizontal width of the wheel and is attached at both ends to the truck body. The "helper" spring is aligned vertically with its lower end attached to the axle and the upper end unattached. The upper end is a distance y0 from the truck body. (a) What is the compression of the leaf spring for a load of 5.50 ✕ 105 N? (b) How much work is done in compressing the springs?

Chapter 7 Solutions

Physics for Scientists and Engineers With Modern Physics

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