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Ch 11: Impulse and Momentum
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Knight Calc 5th EditionCh 11: Impulse and Momentum문제 38
11장, 문제 38

A 550 g cart is released from rest on a frictionless, 30° ramp, 120 cm from the bottom of the ramp. It rolls down, bounces off a rubber block at the bottom, and then rolls 80 cm back up the ramp. A high-speed video shows that the cart was in contact with the rubber block for 25 ms. What was the average force exerted on the cart by the block?

검증된 단계별 안내
1
Step 1: Calculate the initial velocity of the cart just before it hits the rubber block. Use the conservation of energy principle to find the velocity at the bottom of the ramp. The potential energy at the top of the ramp is converted into kinetic energy at the bottom. The formula is: \( m g h = \frac{1}{2} m v^2 \), where \( h \) is the height of the ramp, \( m \) is the mass of the cart, \( g \) is the acceleration due to gravity, and \( v \) is the velocity.
Step 2: Determine the height \( h \) of the ramp using trigonometry. The ramp length is given as 120 cm, and the angle is 30°. Use \( h = L \sin(\theta) \), where \( L \) is the ramp length and \( \theta \) is the angle of inclination.
Step 3: After the cart bounces off the rubber block, calculate the velocity of the cart as it moves back up the ramp. Use the conservation of energy principle again, but this time for the motion after the bounce. The cart rolls back up to a height \( h' \), which can be calculated using \( h' = L' \sin(\theta) \), where \( L' \) is the distance the cart rolls back up the ramp (80 cm). The velocity after the bounce can be found using \( \frac{1}{2} m v'^2 = m g h' \).
Step 4: Calculate the change in velocity \( \Delta v \) of the cart due to the collision with the rubber block. The change in velocity is \( \Delta v = v - v' \), where \( v \) is the velocity before the collision and \( v' \) is the velocity after the collision.
Step 5: Use the impulse-momentum theorem to find the average force exerted on the cart by the block. The impulse-momentum theorem states \( F_{avg} \Delta t = m \Delta v \), where \( F_{avg} \) is the average force, \( \Delta t \) is the contact time (25 ms), \( m \) is the mass of the cart, and \( \Delta v \) is the change in velocity. Rearrange the formula to solve for \( F_{avg} \): \( F_{avg} = \frac{m \Delta v}{\Delta t} \).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
15m
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주요 개념

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

Newton's Second Law of Motion

Newton's Second Law states that the force acting on an object is equal to the mass of that object multiplied by its acceleration (F = ma). This principle is crucial for understanding how forces affect the motion of the cart as it interacts with the rubber block, allowing us to calculate the average force exerted during the collision.
추천 영상:
가이드 코스
06:54
Intro to Forces & Newton's Second Law

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In this scenario, the potential energy of the cart at the top of the ramp is converted into kinetic energy as it rolls down, and this energy transformation is essential for analyzing the cart's motion and the effects of the collision.
추천 영상:
가이드 코스
06:24
Conservation Of Mechanical Energy

Impulse and Momentum

Impulse is defined as the change in momentum of an object when a force is applied over a period of time. The relationship between impulse and momentum is key to determining the average force exerted on the cart by the rubber block, as it involves calculating the change in momentum during the brief contact time of 25 ms.
추천 영상:
가이드 코스
06:00
Impulse & Impulse-Momentum Theorem
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