FIGURE 8-10 An object of mass m is at rest on a rough inclined plane with height h, length 8 m, and which makes an angle of 30° with the horizontal. The object is allowed to move and it stops on a rough horizontal surface, at a distance of 4 m from the bottom of the inclined plane, as shown in Figure 8-10. The coefficient of kinetic friction on the inclined plane is 0.4 and g = 10 m/s 2 .
-Refer to Figure 8-10. What is the speed of the object at the bottom of the inclined plane?

Question

FIGURE 8-10  An object of mass m is at rest on a rough inclined plane with height h, length 8 m, and which makes an angle of 30° with the horizontal. The object is allowed to move and it stops on a rough horizontal surface, at a distance of 4 m from the bottom of the inclined plane, as shown in Figure 8-10. The coefficient of kinetic friction on the inclined plane is 0.4 and g = 10 m/s 2 .
-Refer to Figure 8-10. What is the speed of the object at the bottom of the inclined plane?

Quizplus · Accepted Answer

Using conservation of energy, we can find the speed of the object at the bottom of the inclined plane. The initial potential energy of the object on the inclined plane is mgh, where h is the height of the plane. This potential energy is converted into kinetic energy at the bottom of the plane, where the object has reached its maximum speed. At this point, all of the kinetic energy is lost due to friction, so the final kinetic energy is 0.

Therefore, we have:

mgh = 1/2mv^2
v = sqrt(2gh)

Substituting in the values given:

v = sqrt(2*10*8*sin(30)) = 5 m/s

Therefore, the answer is B.

FIGURE 8-10 an Object of Mass M Is at Rest