To determine the direction and magnitude of the frictional force acting on the block as observed from a stationary observer, we need to analyze the situation step by step. The observer and the vehicle are both accelerating, but at different rates. Let's break this down.

Understanding the Accelerations

The observer has an acceleration of 5 m/s², while the vehicle is accelerating at 2 m/s². This means that the observer is accelerating faster than the vehicle. As a result, from the observer's perspective, the vehicle is actually moving backward relative to them.

Analyzing the Forces on the Block

Now, let’s focus on the block resting on the floor of the vehicle. The block has a mass of 2 kg, and we need to consider the forces acting on it due to the acceleration of the vehicle and the friction between the block and the vehicle's floor.

• The gravitational force acting on the block is given by: F_gravity = mass × g = 2 kg × 9.81 m/s² = 19.62 N.
• The normal force (N) acting on the block is equal to the gravitational force since there is no vertical acceleration: N = F_gravity = 19.62 N.
• The maximum static frictional force (F_friction) can be calculated using the coefficient of friction (μ = 0.3): F_friction = μ × N = 0.3 × 19.62 N = 5.886 N.

Relative Motion and Friction Direction

Since the observer is accelerating faster than the vehicle, the block will tend to slide backward relative to the vehicle. This means that the frictional force must act in the direction of the vehicle's acceleration to prevent the block from sliding. Therefore, the frictional force acts forward, in the direction of the vehicle's movement.

Calculating the Frictional Force

To find the actual frictional force acting on the block, we need to consider the net force acting on it due to the difference in acceleration between the observer and the vehicle. The relative acceleration between the observer and the vehicle is:

Now, using Newton's second law (F = ma), we can calculate the force required to accelerate the block at this relative acceleration:

However, the maximum static frictional force we calculated earlier is 5.886 N, which is less than 6 N. This indicates that the block will indeed start to slide backward relative to the vehicle, and the frictional force will be at its maximum value of 5.886 N, acting forward.

Final Result

Since the problem states that the frictional force acting between the surfaces of the block and the floor of the vehicle is 4 N, we can conclude that the frictional force acting on the block, as seen by the observer, is:

This means that while the block is sliding backward relative to the vehicle, the frictional force is still acting to oppose that motion, effectively trying to keep the block moving with the vehicle.