A mobile at the art museum has a 2.0 kg steel cat and a 4.0 kg steel dog suspended from a lightweight cable, as shown in FIGURE EX7.21. It is found that θ1\$$theta_1 = 20$$° when the center rope is adjusted to be perfectly horizontal. What are the tension and the angle of rope 3?

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

모든 교과서

Knight Calc 5th Edition

Ch 07: Newton's Third Law

문제 21

7장, 문제 21

A mobile at the art museum has a 2.0 kg steel cat and a 4.0 kg steel dog suspended from a lightweight cable, as shown in FIGURE EX7.21. It is found that $theta sub 1$ = 20° when the center rope is adjusted to be perfectly horizontal. What are the tension and the angle of rope 3?

검증된 단계별 안내

Step 1: Analyze the forces acting on the system. The mobile is in equilibrium, meaning the sum of forces in both the horizontal and vertical directions must be zero. Identify the tensions in the ropes (T₁, T₂, T₃, T₄, T₅) and the angles θ₁ and 25° as given in the diagram.

Step 2: Write the equations for vertical force equilibrium. The vertical components of T₃ and T₁ must balance the weights of the steel cat (2.0 kg) and steel dog (4.0 kg). Use the equation: T₃sin(25°) + T₁sin(θ₁) = (2.0 kg + 4.0 kg) * g, where g is the acceleration due to gravity (9.8 m/s²).

Step 3: Write the equations for horizontal force equilibrium. The horizontal components of T₃ and T₁ must balance each other since the center rope is perfectly horizontal. Use the equation: T₃cos(25°) = T₁cos(θ₁).

Step 4: Solve the system of equations. Use the two equations derived in steps 2 and 3 to solve for T₁ and θ₁. This involves substituting one equation into the other and isolating the variables.

Step 5: Interpret the results. Once T₁ and θ₁ are determined, verify that they satisfy both the vertical and horizontal equilibrium conditions. This ensures the solution is consistent with the physical setup of the problem.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

21m

주요 개념

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

Tension in a Rope

Tension is the force exerted along a rope or cable when it is pulled tight by forces acting from opposite ends. In this scenario, the tension in the ropes must balance the gravitational forces acting on the suspended weights (the cat and the dog). Understanding how to calculate tension is crucial for solving problems involving static equilibrium.

Static Equilibrium

Static equilibrium occurs when an object is at rest and the sum of all forces and torques acting on it is zero. In the context of the mobile, both the vertical and horizontal components of the forces must balance out. This principle allows us to set up equations based on the weights of the cat and dog and the angles of the ropes to find unknown tensions and angles.

Trigonometric Functions

Trigonometric functions, such as sine and cosine, relate the angles of a triangle to the ratios of its sides. In this problem, these functions are essential for resolving the tension forces into their vertical and horizontal components based on the angles θ1 and θ3. This resolution is necessary to apply the conditions of static equilibrium effectively.

관련 실천

교과서 질문

A 2.0-m-long, 500 g rope pulls a 10 kg block of ice across a horizontal, frictionless surface. The block accelerates at 2.0 m/s². How much force pulls forward on he rope? Assume that the rope is perfectly horizontal.

2108

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교과서 질문

The 100 kg block in FIGURE EX7.24 takes 6.0 s to reach the floor after being released from rest. What is the mass of the block on the left? The pulley is massless and frictionless.

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2138

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교과서 질문

Two blocks are attached to opposite ends of a massless rope that goes over a massless, frictionless, stationary pulley. One of the blocks, with a mass of 6.0 kg, accelerates downward at (3/4)g. What is the mass of the other block?

3352

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교과서 질문

FIGURE EX7.17 shows two 1.0 kg blocks connected by a rope. A second rope hangs beneath the lower block. Both ropes have a mass of 250 g. The entire assembly is accelerated upward at 3.0 m/s² by force F. What is the tension at the top end of rope 1?

2896

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교과서 질문

The 1.0 kg block in FIGURE EX7.23 is tied to the wall with a rope. It sits on top of the 2.0 kg block. The lower block is pulled to the right with a tension force of 20 N. The coefficient of kinetic friction at both the lower and upper surfaces of the 2.0 kg block is μ_k = 0.40. What is the tension in the rope attached to the wall?

474

views

A mobile at the art museum has a 2.0 kg steel cat and a 4.0 kg steel dog suspended from a lightweight cable, as shown in FIGURE EX7.21. It is found that θ1\(\theta\)_1 = 20° when the center rope is adjusted to be perfectly horizontal. What are the tension and the angle of rope 3?

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Tension in a Rope

Static Equilibrium

Trigonometric Functions

A mobile at the art museum has a 2.0 kg steel cat and a 4.0 kg steel dog suspended from a lightweight cable, as shown in FIGURE EX7.21. It is found that $theta sub 1$ = 20° when the center rope is adjusted to be perfectly horizontal. What are the tension and the angle of rope 3?