Question

Josh has a toy car of mass 3 kg tied to a string of length 2 m. He ties the string to a pole and has the toy car drive in a circle around the pole at a speed of 3 m/s.
a. What is the centripetal acceleration of the car?

b. If the tension in the string exceeds 50 N, the string will break. How fast can he make the car go without breaking the string?

Answer 1

Part a)

Centripetal acceleration is defined as

$a_c = \frac{v^2}{R}$

now here we know that

$v = 3m/s$

$R = 2 m$

m = 3 kg

now from above formula we have

$a_c = \frac{3^2}{2}$

$a_c = 4.5 m/s^2$

Part b)

Maximum possible tension in the string is given as

$T = 50 N$

now by force equation we have

$F = ma$

$50 = 3 a$

$a = \frac{50}{3} m/s^2$

now again by above formula

$\frac{v^2}{R} = \frac{50}{3}$

$v = \sqrt{\frac{50 \times 2}{3}}$

$v = 5.77 m/s$

Answer 2

a) a=v^2/R=4.5 m/s/s

b) F=ma=mv^2/R, so

$v=\sqrt{FR/m}=5.77$ m/s