PLEASE EXPLAIN STEP BY STEP!! a) A toy car of mass m = 5.22 kg goes going around

Question

PLEASE EXPLAIN STEP BY STEP!!

a) A toy car of mass m = 5.22 kg goes going around a circular track of radius r = 3 m every 14.7 seconds. Find F, the magnitude of the inward force needed to keep it moving in a circle.
1 N

b) The same 5.22 kg toy car now starts at rest on the same track, and accelerates at a constant rate to final speed v = 1.14 m/s in time t = 7.18 seconds. At the instant it reaches its final speed, find:

- Fc, the magnitude of the inward force needed to keep it moving in a circle: 2 N
- Ft, the magnitude of the tangential force acting on m: 3 N
- Fnet, the magnitude of the net force acting on m: 4 N

Explanation / Answer

a)
v = 2*pi*r/t = 2*pi*(3m)/(14.7 s) = 1.28 m/s
F = ma
a = v^2/r = (1.28 m/s)^2/(3m) = 0.55 m/s^2
F = (5.22 kg)*(0.55 m/s^2) = 2.86 N

b)
Fc = same as above = mv^2/r = (5.22kg)*(1.14m/s)^2/(3m) = 2.26 N

Ft = ma
vf = at
a = vf/t = (1.14 m/s)/(7.18s) = 0.159 m/s^2
Ft = (5.22kg)*(0.159m/s^2) = 0.823 N

Fnet = SQRT(Fc^2 + Ft^2) = SQRT((2.26 N)^2 + (0.823 N)^2) = 2.41 N

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