A 10 kg cart is attached to a rope that forces the cart to travel along a circular path. The rope has a length of 2.7 meters and has a rotational speed of 2.0 rotations per second.

  F = 4361.7 N

Explanation:

In this exercise the force of the string is asked, to solve it we use Newton's second law

          F - W = m a

force is the tension of the rope

the centripetal acceleration is

        a = v² / r

the angular and linear speed are related

        v = w r

let's substitute

          F - mg = m w² r

          F = m (g + w² r)

let's reduce the magnitudes to the SI system

       w = 2.0 rot / s (2π rad / 1 rev) = 4π  rad / s

let's calculate

       F = 10 (9.8 + (4π)² 2.7)

       F = 4361.7 N

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.