What net force will make a 5 kg bowling ball accelerate by 1.5 m/s square 2?

In pure translation or in roll without slip?

In pure translation, just use Fnet = m*a.  Fnet = 7.5 Newtons

In roll without slip it has effectively more inertia than 5 kilograms.  The effective inertia can be found as:

m_effective = m + I/r^2

For a uniform solid sphere, I = 2/5*m*r^2

So m_effective = 7/5*m

To make a 5 kg bowling ball accelerate at 1.5 m/s^2 in roll without slip, it requires Fnet = 10.5 Newtons, and this ASSUMES that all forces causing the net force on it have lines of action through its center of mass (most common case).

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step-by-step explanation: