Help and please show all work. Answers are 38m/s and 2000N. 3. An apparatus is d

Question

Help and please show all work. Answers are 38m/s and 2000N.

3. An apparatus is designed to study the behavior of ants undergoing higlh acceleration. It consists of a small box containing the ants attached to the end of a 1.5 m string. The other end of the string is held fixed in place and the box is swung along a circular path. The box is swung seo that its centripetal acceleration (radial acceleration) is 980 m/s (and therefore the ants experience an apparent weight that is 100 times normal). Neglect gravity. (a) How fast must the box be moving in m/s in order to achieve this? (b) If the mass of the box is 2 kg and the string has no mass, what is the tension in the string?

Explanation / Answer

here,

length , l = 1.5 m

centripital accelration , a = 980 m/s^2

a)

let the speed of box be v

a = v^2 /l

980 = v^2 / 1.5

solving for v

v = 38 m/s

the final speed is 38 m/s

b)

mass , m = 2 kg

the tension in the cable , T = m * ( g + a)

T = 2 * ( 980 + 9.81) N

T = 2000 N

the tension in the cable is 2000 N

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