Question

John is riding a bicycle and comes across a hill of height 7.30 m. At the base of the hill,
he is traveling at 6.00 m/s. When he reaches the top of the hill, he is traveling at 1.00 m/s.
Jonathan and his bicycle together have a mass of 85.0 kg. Ignore friction in the bicycle
mechanism and between the bicycle tires and the road.
i) What is the total external work done on the system of Jonathan and the bicycle between
the time he starts up the hill and the time he reaches the top?
ii) What is the change in potential energy stored in Jonathan’s body during this process?

Answer 1

Solution.

$h_0=0;$

$h=7.30m;$

$v_0=6m/s;$

$v=1m/s;$

$m=85.0kg;$

i) $W=E_ k ​ −E_ {k0}$;

$W=\dfrac{mv^2}{2}-\dfrac{mv_0^2}{2};$

$W=\dfrac{85.0kg\sdot(1m/s)^2}{2}-\dfrac{85.0kg\sdot(6m/s)^2}{2}=$

$=​−1487.5J= -1.488kJ;$

ii)$\Delta E_p=Ep-E_{p0}$ ;

$\Delta E_p=mgh-mgh_0;$

$\Delta E_p=85.0kg\sdot9.81N/kg\sdot7.30m-0=6087J=$

$=6087J=6.087kJ;$

Answer: i)$W=-1.488kJ$ ;

ii)$\Delta E_p=6.087kJ.$