please solve all the questions 11. (5 points) In the testing of a real spring st
ID: 1403737 • Letter: P
Question
please solve all the questions
11. (5 points) In the testing of a real spring stretched near its elastic limit, the spring force satisfies the equation F = - k delta x + beta(delta x)^3, where delta x is the distance stretched. If k = 10 N/m and beta = 100 N/m^3, calculate the work done by this force when the spring is stretched 0.10 m. 12. (10 points) A 10 - kg crate is placed in the bed of a truck at rest on horizontal ground. The truck accelerates uniformly at 1 m/s^2 for 10 seconds. The crate does not slip during this acceleration. (a) What force does work on the crate during this acceleration? (b) What is the sign of the work done on the crate. (c) What is the coefficient of static friction between the truck bed and the crate?Explanation / Answer
F = - Kx + x^3
Given,
K =10N/m
= 100 N/m^3
Stretch in Spring = 0.10m
We know,
Work done by Force = Force * Distance
Work done for small distanec dx = F*dx
Work done for small distanec dx = (- Kx + x^3) dx
If we want to calculate for 0.10m
We need to Integrate the above expressiopn =
W = 00.1 (- Kx + x^3) dx
W = 00.1- Kx dx + x^3 dx
w = 00.1 -kx^2 /2 + x^4/4
Substituting Vlaues -
w= [-10x^2 /2 + 100x^4/4]0.1
w= -10*0.1^2 /2 + 100 * 0.1^4/4
w= -10*0.1^2 /2 + 100 * 0.1^4/4
w= - 0.0475 J
Work done by the force w= - 0.0475 J
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