Understanding the Problem
* Static Friction: This is the force that prevents an object from moving when it's at rest. It's a maximum force that can be overcome if the applied force is strong enough.
* Kinetic Friction: This is the force that opposes the motion of an object already moving.
* Coefficients of Friction:
* μs (0.64): The coefficient of static friction. This tells us how strongly the surfaces resist the start of motion.
* μk (0.42): The coefficient of kinetic friction. This tells us how strongly the surfaces resist motion once it's already happening.
Steps to Solve
1. Identify the Forces:
* Weight (W): The force due to gravity acting on the block. W = mg, where 'm' is the mass (1 kg) and 'g' is the acceleration due to gravity (approximately 9.8 m/s²).
* Normal Force (N): The force exerted by the surface on the block, perpendicular to the surface. Since the block is on a horizontal surface, N = W.
* Frictional Force (fr): The force that opposes motion. We need to figure out if this is static or kinetic friction.
2. Determine the Type of Friction:
* Since the problem only mentions the force due to gravity, we assume the block is at rest (not moving). Therefore, we're dealing with static friction.
3. Calculate the Maximum Static Friction:
* The maximum force of static friction (fsmax) is calculated as: fsmax = μs * N
* In this case: fsmax = 0.64 * (1 kg * 9.8 m/s²) = 6.272 N
4. Determine the Frictional Force:
* Since the block is at rest, the frictional force is equal to the maximum static friction. This prevents the block from moving.
* Therefore, fr = fsmax = 6.272 N
Answer: The magnitude of the frictional force (fr) acting on the block is 6.272 N.
