Final answer:
The weight of the box is 54.88 N. The weight (parallel) component is 23.66 N, the weight (perpendicular) component is 49.51 N, and the normal force is 49.51 N in the opposite direction. The frictional force is 23.66 N in the opposite direction. The coefficient of friction is 0.477. The net force is 0 N, and the acceleration is 0 m/s^2.
Step-by-step explanation:
To find the weight of the box, we can use the formula W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity. The weight is given by W = 5.60 kg * 9.8 m/s^2 = 54.88 N.
To find the weight (parallel) and weight (perpendicular) components, we can use trigonometry. The weight (parallel) can be found by multiplying the weight by the sine of the angle of the ramp. The weight (parallel) is given by W_parallel = W * sin(23.0°) = 54.88 N * sin(23.0°) = 23.66 N. The weight (perpendicular) can be found by multiplying the weight by the cosine of the angle of the ramp. The weight (perpendicular) is given by W_perpendicular = W * cos(23.0°) = 54.88 N * cos(23.0°) = 49.51 N.
The normal force is equal in magnitude and opposite in direction to the weight (perpendicular) component. Therefore, the normal force is 49.51 N in the opposite direction.
Since the box is at rest, the frictional force must be equal in magnitude and opposite in direction to the weight (parallel) component. Therefore, the frictional force is 23.66 N in the opposite direction.
The coefficient of friction can be found by dividing the frictional force by the normal force. The coefficient of friction is given by µ = F_friction / F_normal = 23.66 N / 49.51 N = 0.477.
The net force can be found by subtracting the frictional force from the weight (parallel) component. The net force is given by F_net = F_parallel - F_friction = 23.66 N - 23.66 N = 0 N.
Since the net force is zero, the acceleration is also zero. Therefore, the acceleration is 0 m/s^2.