If a block is kept on rear side of truck which is accelerating in the forward direction and acceleration is sufficient to cause sliding of the block

When a block is placed on the rear side of a truck that is accelerating forward, several forces come into play that can lead to the block sliding off. To understand this scenario, we need to consider the concepts of inertia, friction, and the forces acting on the block.

Understanding the Forces at Play

When the truck accelerates, it exerts a force on the block due to its acceleration. However, the block has a tendency to remain at rest due to inertia, which is described by Newton's first law of motion. This means that while the truck moves forward, the block wants to stay in its original position unless acted upon by an external force.

The Role of Friction

The frictional force between the block and the truck bed is crucial in determining whether the block will slide. This frictional force can be calculated using the formula:

• Frictional Force (F_f) = μ * N

Here, μ is the coefficient of friction between the block and the surface of the truck bed, and N is the normal force, which is equal to the weight of the block if we assume the truck is on a flat surface.

Acceleration and Sliding Condition

For the block to remain stationary relative to the truck, the frictional force must be sufficient to counteract the force due to the truck's acceleration. The force acting on the block due to the truck's acceleration can be expressed as:

• F = m * a

Where m is the mass of the block and a is the acceleration of the truck. The block will start to slide if the frictional force is less than this force. Therefore, the condition for sliding can be summarized as:

• μ * m * g < m * a

Where g is the acceleration due to gravity. Simplifying this inequality gives:

• μ * g < a

This means that if the acceleration of the truck exceeds the product of the coefficient of friction and the acceleration due to gravity, the block will slide off the rear side of the truck.

Example Scenario

Let’s consider a practical example. Suppose the truck is accelerating at 5 m/s², and the block has a mass of 2 kg. If the coefficient of friction between the block and the truck bed is 0.3, we can calculate the maximum frictional force:

• F_f = μ * N = 0.3 * (2 kg * 9.81 m/s²) = 5.886 N

Now, the force due to the truck's acceleration is:

• F = m * a = 2 kg * 5 m/s² = 10 N

Since 10 N (the force due to acceleration) is greater than 5.886 N (the maximum frictional force), the block will slide off the rear side of the truck.

Conclusion

In summary, when a truck accelerates forward, a block placed on its rear side may slide off if the truck's acceleration exceeds the maximum frictional force that can be exerted between the block and the truck bed. Understanding these forces helps us predict the behavior of objects in accelerating frames of reference.