Question

Students use a stretched elastic band to launch carts of known mass horizontally on a track. The elastic bands exert a force F, which is nonlinear as a function of the distance x that the band is stretched. A meter stick is used to measure x, and a motion detector is used to measure the resulting maximum speed of the carts. This procedure is repeated to gather data for several different values of x. Which of the following graphs, if linear, supports the hypothesis that F is a function of x^2?

a. A graph of the cart's maximum speed as a function of x
b. A graph of the cart's maximum speed as a function of x^2
c. A graph of the cart's maximum speed squared as a function of x
d. A graph of the cart's maximum speed squared as a function of x^2
e. A graph of the cart's maximum speed squared as a function of x^3

Answer 1

Answer:

e. A graph of the cart's maximum speed squared as a function of x^3

Explanation:

F = k x²

work done by F

∫Fdx

= ∫kx²dx

= k x³ / 3

According to work energy theorem

k x³ / 3  = 1/2 mv²

v² is a linear function of x³

option     e) is correct.

Answer 2

A graph of the cart's maximum speed  squared as a function of x^3

Given that a Student stretches  the elastic band with Force F which is nonlinear function of the distance x.

Assuming that F is a function of x^2

$F= Kx^2$

By definition of Work we can say that

$W = F.ds$

W = $\int Kx^2dx$

W= $Kx^3/3$

According to Work Energy theorem Work = Change in Kinetic energy

hence $1/2 \times m\ \times V^2$ = $Kx^3/3$

We can clearly see that

$v^2$ $\alpha$ $x^3$

So we can conclude from the analysis that

A graph of the cart's maximum speed squared as a function of x^3.

Hence Option e is the correct option.

For more information please refer to the link below

https://brainly.com/question/24509770