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Ch 08: Momentum, Impulse, and Collisions
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Young & Freedman Calc 14th EditionCh 08: Momentum, Impulse, and Collisions문제 4b
8장, 문제 4b

Two vehicles are approaching an intersection. One is a 2500-kg pickup traveling at 14.0 m/s from east to west (the -x-direction), and the other is a 1500-kg sedan going from south to north (the +y-direction) at 23.0 m/s. What are the magnitude and direction of the net momentum?

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1
Step 1: Understand the concept of momentum. Momentum is a vector quantity defined as the product of an object's mass and velocity. The formula for momentum is \( \mathbf{p} = m \cdot \mathbf{v} \), where \( m \) is the mass and \( \mathbf{v} \) is the velocity vector.
Step 2: Calculate the momentum of the pickup truck. The pickup truck has a mass of 2500 kg and is traveling at a velocity of 14.0 m/s in the -x direction. Using \( \mathbf{p}_{\text{pickup}} = m \cdot \mathbf{v} \), the momentum vector of the pickup truck is \( \mathbf{p}_{\text{pickup}} = 2500 \cdot (-14.0) \) in the x-direction.
Step 3: Calculate the momentum of the sedan. The sedan has a mass of 1500 kg and is traveling at a velocity of 23.0 m/s in the +y direction. Using \( \mathbf{p}_{\text{sedan}} = m \cdot \mathbf{v} \), the momentum vector of the sedan is \( \mathbf{p}_{\text{sedan}} = 1500 \cdot 23.0 \) in the y-direction.
Step 4: Determine the net momentum vector. Since momentum is a vector quantity, the net momentum \( \mathbf{p}_{\text{net}} \) is the vector sum of the individual momenta: \( \mathbf{p}_{\text{net}} = \mathbf{p}_{\text{pickup}} + \mathbf{p}_{\text{sedan}} \). This involves adding the x-component of the pickup truck's momentum and the y-component of the sedan's momentum.
Step 5: Calculate the magnitude and direction of the net momentum. The magnitude of the net momentum is given by \( |\mathbf{p}_{\text{net}}| = \sqrt{(p_x)^2 + (p_y)^2} \), where \( p_x \) and \( p_y \) are the x and y components of the net momentum. The direction (angle \( \theta \)) can be found using \( \theta = \tan^{-1}(p_y / p_x) \).

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주요 개념

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

Momentum

Momentum is a vector quantity defined as the product of an object's mass and its velocity. It is expressed as p = mv, where p is momentum, m is mass, and v is velocity. Momentum has both magnitude and direction, making it crucial for analyzing collisions and interactions between objects.
추천 영상:
가이드 코스
05:17
Intro to Momentum

Vector Addition

Vector addition is the process of combining two or more vectors to determine a resultant vector. This involves adding the corresponding components of the vectors, taking into account their directions. In the context of momentum, the total momentum of a system is found by vectorially adding the momenta of individual objects.
추천 영상:
가이드 코스
07:30
Vector Addition By Components

Conservation of Momentum

The conservation of momentum principle states that the total momentum of a closed system remains constant if no external forces act on it. This principle is fundamental in collision problems, allowing us to analyze the motion of objects before and after an interaction by equating their total momentum.
추천 영상:
가이드 코스
05:58
Conservation Of Momentum
관련 실천
교과서 질문

Two vehicles are approaching an intersection. One is a 2500-kg pickup traveling at 14.0 m/s from east to west (the -x-direction), and the other is a 1500-kg sedan going from south to north (the +y-direction) at 23.0 m/s. Find the x- and y-components of the net momentum of this system.

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교과서 질문

You are standing on a sheet of ice that covers the football stadium parking lot in Buffalo; there is negligible friction between your feet and the ice. A friend throws you a 0.600-kg ball that is traveling horizontally at 10.0 m/s. Your mass is 70.0 kg. If the ball hits you and bounces off your chest, so afterward it is moving horizontally at 8.0 m/s in the opposite direction, what is your speed after the collision?

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교과서 질문

You are standing on a sheet of ice that covers the football stadium parking lot in Buffalo; there is negligible friction between your feet and the ice. A friend throws you a 0.600-kg ball that is traveling horizontally at 10.0 m/s. Your mass is 70.0 kg. If you catch the ball, with what speed do you and the ball move afterward?

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교과서 질문

To warm up for a match, a tennis player hits the 57.0-g ball vertically with her racket. If the ball is stationary just before it is hit and goes 5.50 m high, what impulse did she impart to it?

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