Ch 07: Newton's Third Law

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 07: Newton's Third Law

문제 15

7장, 문제 15

The sled dog in FIGURE EX7.15 drags sleds A and B across the snow. The coefficient of friction between the sleds and the snow is 0.10. If the tension in rope 1 is 150 N, what is the tension in rope 2?

검증된 단계별 안내

Step 1: Identify the forces acting on each sled. Sled A has a mass of 100 kg, and sled B has a mass of 80 kg. Both sleds experience frictional forces due to the snow, which can be calculated using the formula: \( F_{\text{friction}} = \mu \cdot m \cdot g \), where \( \mu \) is the coefficient of friction (0.10), \( m \) is the mass of the sled, and \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).

Step 2: Calculate the frictional force for sled A. Using the formula \( F_{\text{friction}} = \mu \cdot m \cdot g \), substitute \( \mu = 0.10 \), \( m = 100 \, \text{kg} \), and \( g = 9.8 \, \text{m/s}^2 \). This will give the frictional force acting on sled A.

Step 3: Calculate the frictional force for sled B. Similarly, use the formula \( F_{\text{friction}} = \mu \cdot m \cdot g \), substituting \( \mu = 0.10 \), \( m = 80 \, \text{kg} \), and \( g = 9.8 \, \text{m/s}^2 \). This will give the frictional force acting on sled B.

Step 4: Analyze the forces acting on sled B. The tension in rope 1 (150 N) is pulling sled B forward, while the frictional force calculated in Step 3 is opposing the motion. The net force on sled B can be calculated using \( F_{\text{net}} = T_1 - F_{\text{friction, B}} \), where \( T_1 \) is the tension in rope 1.

Step 5: Determine the tension in rope 2. The tension in rope 2 must overcome the net force acting on sled B (calculated in Step 4) and the frictional force acting on sled A (calculated in Step 2). Use the equation \( T_2 = F_{\text{net, B}} + F_{\text{friction, A}} \) to find the tension in rope 2.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

주요 개념

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

Friction

Friction is the force that opposes the relative motion of two surfaces in contact. It is influenced by the nature of the surfaces and the normal force acting between them. The coefficient of friction, given as 0.10 in this scenario, quantifies the frictional force relative to the normal force, affecting how much force is needed to move the sleds across the snow.

Tension in a Rope

Tension is the force transmitted through a rope or cable when it is pulled tight by forces acting from opposite ends. In this problem, the tension in rope 1 (150 N) affects the sleds' movement and the tension in rope 2, which must be calculated. Understanding how tension distributes through connected objects is crucial for solving problems involving multiple forces.

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = ma). This principle is essential for analyzing the forces acting on the sleds and the dog, allowing us to determine the relationship between the tensions in the ropes and the resulting motion of the sleds.

관련 실천

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교과서 질문

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