Father and Child Cart Spin: Calculating Rope Tension

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To calculate the rope tension for the spinning cart, the father must consider both horizontal and vertical forces acting on the system. The tension formula T = mv²/R is applicable, where m is the total mass, v is the velocity, and R is the radius of the circular path. The conversion from 17 rpm to rad/s was noted to be approximately 1.8 rad/s, leading to a calculated velocity of 3.6 m/s. It is essential to apply Newton's second law to separate the tension into its horizontal and vertical components for accurate results. Properly analyzing these forces will yield the required tension for the cart to maintain its spin.
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An energetic father stands at the summit of a conical hill as he spins his 24 kg child around on a 5.7 kg cart with a 2.0-m-long rope. The sides of the hill are inclined at 24 degrees . He keeps the rope parallel to the ground, and friction is negligible
What rope tension will allow the cart to spin with the 17 rpm?

I know the equation for tension is T= mv^2/R

I tried to convert 17 rpms into rad/s and got 1.8 rad/s I got the velocity as 3.6 m/s. I don't know if I did this right but any feedback or corrections would be greatly appreciated.. Thanks!
 
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You need to split up your tension into horizontal and vertical components. What forces are acting in the horizontal direction, the vertical? Then you can use Newton's second law to solve for the tension.
 

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