Answer:
A) 11.968 m/s
B) 2668.4N
Step-by-step explanation:
Mass of motorcycle (Mm) = 40kg
Mass of Physics major (Mp) = 72kg
Radius (r) = 14.6m
A) Using Newton's second law of motion, the net force at the top of circle is given by;
ΣF = - Ma(c) = -Mv²/r
And so; Resultant(R) = Mg - Ma(c)
Now, R= 0 since it loses contact.
Thus,
Mg - Ma(c) = 0
From above, -Ma(c) = -mv²/r
So we'll get; Mg - M(vmin)²/r = 0
Thus,Mg = M(vmin)²/r
So, g = (vmin)²/r
(vmin)² = rg
Vmin = √rg
Vmin = √(14.6 x 9.81)
Vmin = √143.226 = 11.968 m/s
B) From the earlier equation, the net force acting on the motorcycle is;
R(m) - M(m)g - M(p)g = M(m)a(c) = (M(m)v²)/r
Thus; let's use;
R(m) - M(m)g - M(p)g = (M(m)v²)/r
So;
R(m) = M(m)g + M(p)g + (M(m)v²)/r
R(m) = g[M(m) + M(p)] + (M(m)v²)/r
From the question, v is now double.
So, v = 2 x 11.968 = 23.936
R(m) = 9.81[40 + 72] + [(40 x 23
936²)/14.6]
R(m) = 1098.72 + 1569.68 = 2668.4N