Bicycle Problem Homework: Find Power for 85kg Man on 5.2° Incline

[Fusilli_Jerry89]

Homework Statement

What power must a man of mass 85kg have to bicycle 850m up a hill, inclined at 5.2 degrees to the horizontal, at a constant speed of 15.6 m/s? The force of friction on the man and the bicycle is 175N parallel to the incline.

Homework Equations

Fnet=ma
W=delta E

The Attempt at a Solution

I do not know where to start because i do not know the mass of the bicycle.

 

[e(ho0n3]

I think you can neglect the mass of the bicycle. To be on the safe side though, just pick a variable to represent the mass of the bicycle and proceed.

 

[m2003]

As a scientist, it is important to accurately define and gather all necessary information before attempting to solve a problem. In this case, we are given the mass of the man (85kg), the distance (850m), the speed (15.6 m/s), and the force of friction (175N). However, the mass of the bicycle is not given.

In order to solve this problem, we need to consider the work-energy theorem, which states that the work done by all forces acting on an object is equal to the change in the object's kinetic energy. In this case, the work done by the man's power will be equal to the change in kinetic energy of the man and the bicycle.

To find the power, we can use the equation P = W/t, where P is power, W is work, and t is time. We can rearrange this equation to solve for work by multiplying both sides by t, giving us W = Pt.

Next, we need to find the work done by the man's power. Since the man is moving at a constant speed, there is no change in kinetic energy and therefore no work done by his power. This means that the work done by the man's power is equal to zero.

Now, we can use the work-energy theorem to set up an equation:

W = Fd cosθ

Where W is work, F is the force applied, d is the distance, and θ is the angle between the force and the direction of motion. In this case, the force applied is the force of friction (175N) and the distance is the vertical distance traveled (850m sin5.2°).

Plugging in the values, we get:

W = (175N)(850m sin5.2°) = 1,420.98 J

Since we know that the work done by the man's power is equal to zero, we can set this value equal to the work done by the frictional force:

1,420.98 J = Fd cosθ

We can solve for F by dividing both sides by the distance (850m sin5.2°) and the cosine of the angle (cos5.2°).

F = 1,420.98 J / (850m sin5.2° cos5.2°) = 175.14 N

Now, we can use the equation F=ma to