Final answer:
The cart's acceleration when rolling friction is neglected is approximately 9.02 m/s^2.
Step-by-step explanation:
The cart's acceleration when rolling friction is neglected can be found using the force of gravity component along the incline. The force acting down the incline is given by:
F = m * g * sin(theta)
where m is the mass of the cart, g is the acceleration due to gravity, and theta is the angle of the incline.
Substituting the given values, we have:
F = 50 kg * 9.8 m/s^2 * sin(64°)
Solving for F, we get:
F = 450.94 N
Since the force of gravity component is the only force acting down the incline, it is also equal to the net force acting on the cart, which is given by:
F = m * a
where a is the acceleration of the cart.
Substituting the mass and solving for a, we find:
a = F / m
a = 450.94 N / 50 kg
a ≈ 9.02 m/s^2