Q. 68

Expert-verifiedFound in: Page 203

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

The father of Example 8.2 stands at the summit of a conical hill as he spins his 20 kg child around on a 5.0 kg cart with a 2.0-m-long rope. The sides of the hill are inclined at 20^{o}. He again keeps the rope parallel to the ground, and friction is negligible. What rope tension will allow the cart to spin with the same 14 rpm it had in the example?

The tension on the rope is 185.4 N.

Total mass of cart and child, m=20+5=25 kg

Radius of the rope, r=2 mAngle of the hill, θ=20^{o} Angular speed, N=14 rpm

First draw the Free body diagram from the given information

Angular velocity is calculated by

Substitute the values, we get

From the figure we can equate the horizontal forces to calculate tension

substitute the values, we get

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