Two blocks of the same mass but made of different material slide across a horizontal, rough surface and eventually come to rest. A graph of the kinetic energy of each block as a function of position along the surface . Which of the following is a true statement about the frictional force Ff that is exerted on the two blocks?
a. Fr=2F8, since the force of friction is represented as the slope for each of the two curves.
b. Fr.-12Fri, since the force of friction is represented as the inverse slope for each of the two curves.
c. Ff:=2Ffi, since the force of friction is represented as the inverse of the area bound by each curve and th horizontal axis.
d. Fe=1/2Fr., since the force of friction is represented as the area bound by each curve and the horizontal axis.

a. [tex]\mathbf{F_{f_2} = 2 F_{f1}}[/tex], [tex]\mathbf { since \ the \ force \ o f \ friction \ is \ represented \ as \ the \ slope \ for \ each \ of \ the \ two \ curves.}[/tex]

Explanation:

From the information given;

Using the work-energy theorem

ΔKE = W = [tex]\mathbf{ F_f \times r}[/tex]

K = [tex]\mathbf{ F_f \times r}[/tex]

∴

[tex]\dfrac{K_1}{K_2} = \dfrac{F_{f1}}{F_{f2}} (\dfrac{r_1}{r_2})[/tex]

Since [tex]K_1 = K_2[/tex] and r_1 = 4, and r_2 = 2 (from the missing diagram which is attached below)

Then;

[tex]1 = \dfrac{F_{f1}}{F_{f2}} (\dfrac{4 \ m}{2 \ m})[/tex]

[tex]\mathbf{F_{f_2} = 2 F_{f1}}[/tex]