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

• Fusilli_Jerry89
In summary, to determine the power required for a man of mass 85kg to bicycle 850m up a 5.2 degree inclined hill at a constant speed of 15.6 m/s, the force of friction of 175N parallel to the incline must be considered. The equations Fnet=ma and W=delta E can be used to solve for the power, though the mass of the bicycle can be neglected or represented by a variable.
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.

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.

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.

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

1. How do I calculate the power required for an 85kg man on a 5.2° incline?

The power required for an 85kg man on a 5.2° incline can be calculated using the formula: Power = Force x Velocity. In this case, the force can be calculated by multiplying the weight (mg) by the sine of the incline angle. The velocity can be calculated using the formula: Velocity = Distance / Time. Therefore, the power required can be calculated by multiplying the weight by the sine of the incline angle and the velocity.

2. What is the weight of an 85kg man?

The weight of an 85kg man is simply 85kg. This is the mass of the man multiplied by the acceleration due to gravity (9.8m/s²).

3. How do I calculate the force on a 5.2° incline?

The force on a 5.2° incline can be calculated using the formula: Force = Weight x sin(incline angle). This is because the weight of the object is being pulled towards the center of the Earth, and this force can be split into two components - one perpendicular to the incline and one parallel to the incline. The force parallel to the incline is what we are interested in, and it can be calculated using the sine of the incline angle.

4. Can I use this formula for any incline angle?

Yes, you can use this formula for any incline angle as long as you are using the correct units (e.g. weight in Newtons, incline angle in radians). If you are using degrees for the incline angle, make sure to convert it to radians first by multiplying by π/180.

5. How accurate is this calculation?

This calculation is based on simplified physics principles and does not take into account factors such as air resistance or rolling resistance. Therefore, it may not be completely accurate in real-world situations. However, it can provide a good estimate of the power required for a person on an incline.

Replies
4
Views
2K
Replies
2
Views
3K
Replies
8
Views
2K
Replies
8
Views
2K
Replies
1
Views
2K
Replies
1
Views
2K
Replies
2
Views
1K
Replies
2
Views
944
Replies
3
Views
4K
Replies
14
Views
2K