Answer: a) 56,550 J b) 30.1 m/s c) 321 m
Explanation:
a) By definition, work, is the process that does an applied force, in order to produce a displacement in the same direction than the applied force, and can be written as follows;
W = F. d. (scalar product of two vectors)
In this case, as the force is parallel to the displacement, work is directly equal to the product of the applied force times the displacement (in magnitude), so we can write the following:
W = F. D = 195 N. 290 m = 56,550 J
b) In absence of friction, the work done by the force is equal to the change in the kinetic energy, as it can be showed using the work-energy theorem.
So, in this case, we can put the following:
W = ΔK ⇒F. D = 1/2 mv²
Solving for v, we get:
v=√2.F.D/m = 30.1 m/s
c) Now, if we assume that there is no friction between the bike and the ground, all the kinetic energy must become gravitational potential energy, at some height h.
We can write the following equation
m.g. h = 1/2 mv²
Simplifying, and taking g = 9.8 m/s², we can find h:
h= 46.2 m
Now, we need to know the distance travelled up the incline, which is related with the height h, by the angle that the incline does with the horizontal, as follows:
sin 8.29° = h /d ⇒ d= h / sin 8.29° = 46.2 m / sin 8.29° = 321 m
