Final answer:
The net force on the couch is 56.65N and the magnitude of acceleration is 0.38 m/s^2.
Step-by-step explanation:
To determine the net force on the couch, we need to consider the forces acting on it. The girl applies a force of 300N at an angle of 20° above the horizontal. We can break this force into its horizontal and vertical components using trigonometry. The vertical component does not affect the horizontal motion of the couch, so we only consider the horizontal component. The horizontal component of the force can be found using the equation F_h = F * cos(theta), where F is the magnitude of the force and theta is the angle. Therefore, the horizontal component of the force is F_h = 300N * cos(20°) = 277.15N.
The net force on the couch is the difference between the applied force and the force of friction. The force of friction can be found using the equation F_friction = μ * N, where μ is the coefficient of kinetic friction and N is the normal force. The normal force is equal to the weight of the couch, which is the mass of the couch times the acceleration due to gravity. The acceleration due to gravity is approximately 9.8 m/s^2. Therefore, N = 150Kg * 9.8 m/s^2 = 1470N. The force of friction is F_friction = 0.15 * 1470N = 220.5N.
The net force on the couch is the applied force minus the force of friction. Therefore, the net force on the couch is F_net = F_h - F_friction = 277.15N - 220.5N = 56.65N.
To find the magnitude of acceleration, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object times its acceleration. Rearranging this equation gives us a = F_net / m, where a is the acceleration, F_net is the net force, and m is the mass of the object. Plugging in the values, we get a = 56.65N / 150Kg = 0.38 m/s^2. Therefore, the magnitude of acceleration is 0.38 m/s^2.