bicyclist increases its velocity at constant power
a) how great is this power when the bicycle's velocity increases, from 18km/h to 23km/h, during the time of 1,2 seconds
b) Within which boundaries does the acceleration vary? The combined mass of bicyclist and his bicycle is 78kg
delta E= W
0,5 * m * v^2 = Ekin
The Attempt at a Solution
I assumed the same mass of bycyle as it was described in the later b) portion of the problem. Assume mass = 78kg
The problem looks like very difficult to solve, without assuming the mass to be 78kg. I wonder whether it is possible to calculate the power, without this beginning assumption.
transform velocities into m/s
v0= 5 m/s (nice that it divided evenly by 3,6!)
v1= 6,388 m/s
delta Ekinetic = Work
work = 616,4552 joules
assuming flat ground during travelling.
P= 616,4552 joules / 1,2 s
P= 513,71 Watts
roughly 510 Watts (correct answer according to book answer, in this sense)
b) Within which boundaries does bicycles acceleration vary?
I have no idea how to strictly speaking answer the b) part
I suppose one could examine the velocities v0 and v1.
It is known that v0= 5m/s and v1= 6,388m/s
I backtracked in my textbook and found a formula which seems useful in this case. I must have glazed over this formula or simply misunderstood the formula earlier.
Ok according to my physics book one can calculate thusly
power at instant = (force at instant) * (velocity at instant)
We already calculated the power which was 510 Watts.
If we assume constant power, then we could use
P = F * v
510 W = F1* 5 m/s
510 W = F2 * 6,388 m/s
F1= 102 N
F2= 79, 8371 N
Then we can know already the mass, and the forces F1 and F2.
We can calculate a1 and a2
F2= m * a2
a1= 102N / 78kg
= 1,3076 m/s^2
a2= 79,8371 N / 78kg