운동량, 충격량 및 포물체 운동 – 문제 및 해법

운동량, 충격량 및 포물체 운동 – 문제 및 해법

1. 아래 그림과 같이 0.2kg의 공을 구멍 C에 넣으려고 합니다. 타자가 공을 치는 데 0.01초가 걸렸고, 공이 구멍 BC를 따라 이동하는 데 1초가 걸렸습니다. 공을 구멍 C에 넣기 위해 필요한 힘의 크기를 구하세요. 중력에 의한 가속 10m/s입니다.².

알려진 바에 따르면:

각도(θ) = 60^o

질량 공의 질량(m) = 0.2 kg

중력 가속도(g) = 10 m/s²²

시간 간격(Δt) = 0.01초

Time interval to travel path B-C (t) = 1 second

구함: 힘(F)

솔루션 :

방정식 충격 : I = F Δt

Equation of the change in 기세 : Δp = m (v_t - V_o).

The impulse equals the change in momentum :

I = Δp

F Δt = m (v_t - V_o)

F = m (v_t - V_o) / Δt

알려진 바에 따르면:

Δt = 0.01 second

m = 0.2kg

v_t = the final speed in the equation of impulse-momentum = the initial speed of ball (v_o) in the projectile motion

v_o = the initial speed in the equation of impulse-momentum = 0 m/s (initially ball at rest)

F = m (v_t - V_o) / Δt

F = 0.2 (v_t – 0) / 0.01

F = 0.2 v_t / 0,01

계속......

Determine the initial speed of the ball (v_o) in projectile motion

Since the ball is hit until the ball reaches the point B = part 1 of the 발사체 운동.

The ball travels from point B to C = part 2 of the projectile motion.

Part 2 of the projectile motion :

The projectile motion could be understood by analyzing the horizontal and vertical component of the motion separately. The x motion occurs at a constant velocity and the y motion occurs at a constant acceleration of gravity.

알려진 바에 따르면:

Horizontal distance (x) = 5 meters

Time in air (t) = 1 second

x and t are known so that v_ox can calculated using the equation of the 균일한 직선 운동. V_ox is the horizontal component of initial speed of ball.

v_ox = x / t = 5 meters / 1 second = 5 m/s.

Part 1 of the projectile motion :

The horizontal component of speed, v_ox is always same so v_ox in part 1 of the projectile motion = v_ox in part 2 of the projectile motion = 5 m/s.

알려진

v_ox = 5m/s

θ = 60^o

v_ox and θ are known so the initial speed (v_o) can be calculated.

cos θ = adj / hyp

cos θ = v_ox / V_o

v_o = v_ox / cos θ = 5 / cos 60^o = 5 / 0.5 = 10 m/s

초기 속도(v)_o) is 10 m/s.

The initial speed of the ball (v_o) in projectile motion = the final speed of the ball (v_t) in the equation of impulse-momentum.

Determine the magnitude of force (F)

F = 0.2 v_t / 0.01

F = 0.2 (10) / 0.01

F = 2 / 0.01

F = 200 뉴턴

1. What is the relationship between impulse and change in momentum?
   • 답변 : Impulse is the product of force and the time over which it acts, and it is equal to the change in momentum of an object. Mathematically, $Impulse=\Delta p$어디로 $\Delta p$ 운동량의 변화입니다.
2. How does an increase in the time of impact, such as with a crumple zone in a car, affect the force experienced during a collision?
   • 답변 : Increasing the time of impact reduces the average force experienced during a collision. This is because impulse (change in momentum) is constant for a given collision, and by increasing time, the force is spread out over a longer duration, hence decreasing the average force.
3. What remains constant for a projectile in motion under the influence of gravity alone?
   • 답변 : The horizontal velocity of a projectile remains constant when only gravity acts on it. The vertical velocity, however, changes due to gravitational acceleration.
4. Why is the path of a projectile under the influence of gravity parabolic?
   • 답변 : The path is parabolic because while the horizontal velocity remains constant, the vertical velocity is constantly changed by gravitational acceleration, leading to a quadratic relationship between horizontal and vertical displacements.
5. What happens to the momentum of an isolated system if no external forces act on it?
   • 답변 : If no external forces act on an isolated system, its total momentum remains conserved. This is known as the conservation of momentum.
6. How does the impulse provided by a baseball bat to a ball compare when the ball is hit for a home run versus when it’s just tapped lightly?
   • 답변 : The impulse provided to the baseball is greater when hit for a home run compared to when it’s tapped lightly, as the change in momentum of the ball (from stationary to flying off the bat) is much greater in the home run scenario.
7. If a projectile is launched from ground level at an angle and returns to ground level, how do its launch and landing speeds compare?
   • 답변 : Assuming no air resistance, the projectile’s landing speed will be equal to its launch speed. This is due to the conservation of energy.
8. How do the launch angle and range of a projectile relate, assuming no air resistance?
   • 답변 : For a given initial speed, the maximum range of a projectile is achieved at a launch angle of 45 degrees. Launching at angles less or greater than 45 degrees will result in a shorter range.
9. Why does increasing the time over which a force acts on an object, such as catching an egg with a slight hand movement, reduce the likelihood of breaking or damaging the object?

• 답변 : Increasing the time over which a force acts spreads the impulse (change in momentum) over a longer duration, thereby reducing the average force experienced by the object. By catching an egg with a slight hand movement, the force of the catch is spread out, reducing the chance of the egg breaking.