A 1.0 kg wood block is pressed against a vertical wood wall by the 12 N force shown in FIGURE P6.57. If the block is initially at rest, will it move upward, move downward, or stay at rest?

검증된 단계별 안내

Step 1: Identify the forces acting on the block. The forces include the gravitational force (weight), the applied force (12 N), and the frictional force between the block and the wall. The gravitational force is given by \( F_g = m \cdot g \), where \( m = 1.0 \, \text{kg} \) and \( g = 9.8 \, \text{m/s}^2 \).

Step 2: Determine the direction of the forces. The gravitational force \( F_g \) acts downward, while the applied force \( F_a = 12 \, \text{N} \) is horizontal, pressing the block against the wall. The frictional force opposes the motion and can act either upward or downward depending on the situation.

Step 3: Calculate the maximum static friction force. The static friction force is given by \( F_{f, \text{max}} = \mu_s \cdot F_n \), where \( \mu_s \) is the coefficient of static friction for wood on wood (typically \( \mu_s \approx 0.5 \)) and \( F_n \) is the normal force. Here, \( F_n \) is equal to the applied force \( F_a \).

Step 4: Compare the gravitational force \( F_g \) with the maximum static friction force \( F_{f, \text{max}} \). If \( F_g \) is less than or equal to \( F_{f, \text{max}} \), the block will stay at rest. If \( F_g \) exceeds \( F_{f, \text{max}} \), the block will move downward.

Step 5: Conclude the motion of the block. Based on the comparison in Step 4, determine whether the block stays at rest, moves upward, or moves downward. Note that the applied force does not have a vertical component, so it cannot cause upward motion directly.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Newton's First Law of Motion

Newton's First Law states that an object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity unless acted upon by a net external force. In this scenario, the wood block will not move unless the forces acting on it result in a net force that is not zero.

Forces Acting on the Block

To determine the block's motion, we must analyze the forces acting on it. The 12 N force is applied horizontally, while the weight of the block (approximately 9.8 N downward) and any frictional forces between the block and the wall must also be considered. The balance of these forces will dictate whether the block moves or remains stationary.

Friction

Friction is the force that opposes the relative motion of two surfaces in contact. In this case, the friction between the wood block and the wall can prevent the block from sliding down. The maximum static frictional force can be calculated using the coefficient of friction and the normal force, which is influenced by the applied force and the weight of the block.