Question

To avoid falling over,a cyclist needs to maintain speed of about 3 mph. Consider a 180 lb rider on a 20 lb bike attempting the famous 31.5% slope of FIlbert Street in San Francisco. Wind drag and rolling friction certainly aren't his main concerns! We'll ignore them.

a) In pounds, what is the backward force of the hill?

b) How much power must he put out to climb the hill at a constant speed of 3 mph?

c) Refer to the NASA estimate. About how long could a "healthy man" continue such a climb?

Answer 1

Solution a)

Look at the above fig. in which how a rider is trying to go uphill. Here m is the mass of Rider and Bike which is 180lb + 20 lb = 200 lbs and g is acceleration due to gravity 21.63 lb/s2.

The force "mg"due to gravity is acting perpendicular to the Ground OA shown in the above fig.

The slope of the hill is given 17.50

The component of the force mg acting perpendicular to the plane of the hill is in the downward direction.

The component of the force mg acting parallel to the plane of the hill is in the backward direction.

So the backward force of the hill (in pounds) = = 200 lbs x sin(17.5) = 60 lbs (approx)

Ans : The Backward force of the hill, in pounds = 60.0 lbs

Solution b)

We know that power required to climb the hill at a constant speed (v=3 mph ) P (watt)= Backward force (in Newton) X Velocity (m/s)

v = 3 mph = 4.82 kmph = 1.34 m/s

m = 200 lbs = 90.72 kg

g = 9.8 m/s2

sin17.5o = 0.3

Solution C)

According to the NASA estimate a healthy man can spends 8.37 x 106 Joules.

We know that

.................................(1)

So Inorder to continue climbing the hill of slope 31.5% at constant speed of 3 mph or 1.34 m/s, the rider requires 357.4 Watt of power.

According to NASA, a healthy man can do a work equivalent to 8.37 x 106 Joules.

Putting value of power and work done in above equation (1)

Ans: The Time taken by a healthy man to climb the given hill is 6.5 Hours with a constant speed of 3mph.