Ch 10: Interactions and Potential Energy

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

Knight Calc 5th Edition

Ch 10: Interactions and Potential Energy

문제 40

10장, 문제 40

A cable with 20.0 N of tension pulls straight up on a 1.50 kg block that is initially at rest. What is the block's speed after being lifted 2.00 m? Solve this problem using work and energy.

검증된 단계별 안내

Step 1: Identify the forces acting on the block. The upward force is the tension in the cable (20.0 N), and the downward force is the gravitational force, which can be calculated as \( F_g = m \cdot g \), where \( m = 1.50 \; \text{kg} \) and \( g = 9.8 \; \text{m/s}^2 \).

Step 2: Determine the net force acting on the block. The net force is given by \( F_{\text{net}} = F_T - F_g \), where \( F_T \) is the tension in the cable and \( F_g \) is the gravitational force.

Step 3: Calculate the work done by the net force. Work is defined as \( W = F_{\text{net}} \cdot d \), where \( d = 2.00 \; \text{m} \) is the distance the block is lifted. Ensure that the direction of the net force and displacement are aligned.

Step 4: Relate the work done to the change in kinetic energy using the work-energy theorem, \( W = \Delta KE \). Since the block starts from rest, \( \Delta KE = \frac{1}{2} m v^2 \), where \( v \) is the final speed of the block.

Step 5: Solve for the final speed \( v \) by rearranging the equation \( W = \frac{1}{2} m v^2 \) to \( v = \sqrt{\frac{2W}{m}} \). Substitute the values of \( W \) and \( m \) to find the final speed.

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주요 개념

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

Work-Energy Principle

The Work-Energy Principle states that the work done on an object is equal to the change in its kinetic energy. In this context, the work done by the tension in the cable on the block will increase its kinetic energy as it is lifted. This principle allows us to relate the force applied, the distance moved, and the resulting speed of the block.

Gravitational Potential Energy

Gravitational potential energy (PE) is the energy an object possesses due to its position in a gravitational field. It is calculated using the formula PE = mgh, where m is mass, g is the acceleration due to gravity, and h is the height. As the block is lifted, its potential energy increases, which must be accounted for when calculating the total energy changes in the system.

Kinetic Energy

Kinetic energy (KE) is the energy of an object due to its motion, given by the formula KE = 0.5mv², where m is mass and v is velocity. In this problem, as the block is lifted and work is done on it, its kinetic energy will increase, allowing us to determine its speed after being lifted a certain distance by equating the work done to the change in kinetic energy.

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