Askiitians Tutor Team
Last Activity: 4 Months ago
To determine the frictional force acting on the block, we can indeed approach the problem using two different methods: the formula for friction and a free body diagram (FBD). However, it's essential to understand the context of the situation to choose the most suitable method. Let's break it down step by step.
Understanding the Problem
We have a block of mass 1 kg on a truck that is accelerating at 5 m/s². The coefficient of static friction (μ) between the block and the surface is 0.6. The goal is to find the frictional force acting on the block.
Method 1: Using the Friction Formula
The frictional force can be calculated using the formula:
f = μ * M * g
Where:
- f = frictional force
- μ = coefficient of static friction (0.6)
- M = mass of the block (1 kg)
- g = acceleration due to gravity (approximately 9.81 m/s²)
Plugging in the values:
f = 0.6 * 1 kg * 9.81 m/s² = 5.886 N
Method 2: Free Body Diagram (FBD)
In this method, we analyze the forces acting on the block. The block experiences:
- A gravitational force downward: F_gravity = M * g = 1 kg * 9.81 m/s² = 9.81 N
- A normal force upward, which balances the gravitational force.
- A frictional force that opposes the motion due to the truck's acceleration.
Since the truck is accelerating, the block will also experience a pseudo force in the opposite direction of the truck's acceleration. This force can be calculated as:
F_pseudo = M * a = 1 kg * 5 m/s² = 5 N
For the block to remain stationary relative to the truck, the frictional force must equal this pseudo force. Therefore, the frictional force is:
f = 5 N
Comparing the Methods
Both methods yield different results: 5.886 N from the friction formula and 5 N from the FBD method. The discrepancy arises because the friction formula calculates the maximum static friction force, while the FBD method considers the actual force needed to keep the block from sliding.
Which Method to Use?
The FBD method is more suitable in this scenario because it directly addresses the forces acting on the block due to the truck's acceleration. It provides a clearer picture of the dynamics involved, especially since the block is not sliding but rather experiencing a force due to the truck's motion.
Final Thoughts
In summary, while both methods are valid, the FBD approach gives a more accurate representation of the situation at hand. It’s crucial to analyze the context of the problem to determine which method will yield the most relevant results. Understanding the forces at play will help you apply these concepts effectively in various physics problems.
