Question

A 300 g block on a 56-cm-long string swings in a
circle on a horizontal, frictionless table at 70 rpm.

What is the speed of the block?
Express your answer using two significant figures.

What is the tension in the string?
Express your answer using two significant figyres.

Answer 1

Hi there!

We can begin by converting rpm to tangential velocity.

1 rotation = 2πR

Convert min to sec: 1 min = 60 sec

$\frac{70rev}{min} * \frac{2(0.56)\pi m} {1rev} * \frac{1 min}{60 s} = \boxed{4.11 \frac{m}{s}}}$

We can find the tension by using the equation for Centripetal motion.

$T = \frac{mv^2}{r}$

T = Tension (? N)
m = mass (.3 kg)
v = velocity (4.11 m/s)

r = radius (0.56 m)

Plug in the values:

$T = \frac{.3(4.11^2)}{0.56} \approx \boxed{90.27 N}$