תנועת נפילה חופשית - בעיות ופתרונות

תנועת נפילה חופשית - בעיות ופתרונות

1. A stone free fall from the height of 45 meters. If the תאוצה עקב כוח הכבידה is 10 ms^-2, what is the speed of the stone when hits the ground?

ידוע:

גובה (h) = 45 מטרים

תאוצה עקב כוח הכבידה (g) = 10 מטר/שנייה²

מבוקש: The final velocity of the stone when it hits the ground (v_t)

פתרון:

המשוואה של תנועת נפילה חופשית :

v_t² = 2 ג'יגה-הרץ

The final velocity of the stone :

v_t² = 2 (10)(45) = 900

v_t = √900 = 30 m/s²

2. An object free fall from a height without the initial velocity. The object hits the ground 2 seconds later. Acceleration due to gravity is 10 ms^-2. Determine height

ידוע:

מרווח זמן (t) = 2 שניות

תאוצה עקב כוח הכבידה (g) = 10 מטר/שנייה²

מבוקש: גובה (ח)

פתרון:

The equation of the free fall motion :

שעה = ½ ג'ינט²

גובה:

h = ½ (10)(2)² = (5)(4) = 20 מטרים

3.A 2-kg object free fall from a height of 20 meters above the ground. What is the time interval the object in air ? Acceleration due to gravity is 10 ms^-2

ידוע:

גובה (h) = 20 מטרים

תאוצה עקב כוח הכבידה (g) = 10 מטר/שנייה²

רצה : מרווח זמן (t)

פתרון:

The equation of free fall motion :

שעה = ½ ג'ינט²

Time interval :

20 = ½ (10)(t²)

20 = (5)(t²)

20/5 = t²

4 = t²

t = √4

t = 2 שניות

4. Two objects, object 1 and object 2, are free fall from a height of h₁ ו₂ at the same time. If h₁ : ח₂ = 2: 1, what is the ratio of the time interval of the object 1 to the object 2.

ידוע:

The height of the object 1 (h₁) = 2

The height of the object 2 (h₂) = 1

Acceleration due to gravity = g

מבוקש: t₁ :ת₂

פתרון:

Object 1 :

h₁ = 1/2 g t₁²

2 = 1/2 g t₁²

(2)(2) = g t₁²

4 = g t₁²

4/g = t₁²

t₁ = √4/g

Object 2 :

h₂ = 1/2 g t₂²

1 = 1/2 g t₂²

(2)(1) = g t₂²

2 = g t₂²

2/g = t₂²

t₂ = √2/g

The ratio of the time interval :

t₁ :ת₂

√4/g : √2/g

(√4/g)² : (√2/g)²

4/g : 2/g

4: 2

2: 1

5. An object dropped from a height of h above the ground. The final velocity when object hits the ground is 10 m/s. What is the time interval to reach ½ h above the ground. Acceleration due to gravity is 10 m/s².

ידוע:

The final velocity (v_t) = 10 מטר/שנייה

תאוצה עקב כוח הכבידה (g) = 10 מטר/שנייה²

מבוקש: The time interval to reach 1/2 h above the ground

פתרון:

The height of h :

v_t² = 2 ג'יגה-הרץ

10² = 2 (10) h

100 = 20 שעות

h = 100/20

h = 5 מטרים

The height of 1/2 h = 1/2 (5 meters) = 2.5 meters. The time interval needed to reach 2.5 meters above the ground :

h = 1/2 gt²

2.5 = 1/2 (10) טון²

2.5 = 5 טון²

t² = 2.5 / 5 = 0.5 = (0.25)(2)

t = √(0.25)(2) = 0.5√2 = 1/2 √2 seconds

6.

The free fall motion of coconut (איור 1) and the motion of a ball thrown vertically upמחלקה to the highest point by a student (figure 2). Determine the סוג של שניהם תנועהs.

פתרון:

Figure 1 = תנועת נפילה חופשית = Acceleration

Figure 2 = תנועה אנכית = Deceleration

התשובה הנכונה היא A.

7. A stone free fall from a building. The time interval needed by a stone to reach the ground is 3 seconds and acceleration due to gravity is 10 m/s². Determine the height of the building.

א. 15 מטר

ב. 20 מטר

כ-30 מטר

45 מטר ד.

ידוע:

מרווח זמן (t) = 3 שניות

Acceleration due to gravity (g) = 10 m.s^-2

מבוקש: Height of building (h)

פתרון:

Known: time interval (t) and acceleration due to gravity (g), wanted: height (h) so use the equation of free fall motion: h = ½ g t²

h = ½ (10)(3)

h = (5)(3)

h = 15 metes

התשובה הנכונה היא A.

8. A fruit free fall from its tree at the height of 12 m above the ground. If acceleration due to gravity is g = 10 m/s² and the friction of air ignored, then determine the height of the fruit above the ground after 1 second.

א. 7 מטר

ב. 6 מטר

כ-5 מטר

4 מטר ד.

ידוע:

Height of tree (h) = 12 meters

תאוצה עקב כוח הכבידה (g) = 10 מטר/שנייה²

מרווח זמן (t) = שנייה אחת

מבוקש: The height of the fruit above the ground

פתרון:

After 1 second, fruit free fall as far as :

שעה = ½ ג'ינט² = ½ (10)(1)² = (5)(1) = 5 מטרים

The height of the fruit above the ground after 1 second :

12 meters – 5 meters = 7 meters

התשובה הנכונה היא A.

1. What is free fall motion?

   תשובה: Free fall motion refers to the motion of an object under the influence of gravitational force only, with no other forces (like air resistance) acting on it.

2. How does the acceleration due to gravity, often represented as $g$, affect a freely falling object?

   תשובה: All objects in free fall near the surface of the Earth experience a constant acceleration due to gravity, $g$, שזה בערך 9.81גברת² downward. This means that the object’s velocity increases by this amount for each second of free fall.
3. If air resistance is negligible, how does the mass of an object influence its free fall acceleration?

   תשובה: In the absence of air resistance, the mass of an object does not influence its free fall acceleration. All objects, regardless of their mass, will fall with the same acceleration due to gravity, $g$.
4. Why do astronauts appear to float inside the International Space Station (ISS) if gravity is still present there?

   תשובה: Astronauts inside the ISS appear to float not because there’s no gravity, but because both the astronauts and the ISS are in a continuous state of free fall around the Earth. They’re essentially falling at the same rate as the ISS, creating a sensation of weightlessness.

5. What is the difference between weight and mass in the context of free fall?

   תשובה: Mass is a measure of the amount of matter in an object and remains constant regardless of its location. Weight, on the other hand, is the force exerted on an object due to gravity. It varies depending on the gravitational field. During free fall, an object feels weightless because there’s no normal force acting on it, but its mass remains unchanged.
6. If an object is thrown upwards, what happens to its velocity as it rises? And what happens when it starts falling back down?

   תשובה: When an object is thrown upwards, it decelerates under the influence of gravity. Its velocity decreases until it becomes zero at its highest point. As it starts falling back down, it accelerates due to gravity, increasing its velocity in the downward direction.
7. What is terminal velocity in the context of free fall?

   תשובה: Terminal velocity is the constant maximum velocity reached by a falling object when the downward force of gravity is balanced by the upward force of air resistance. At this point, the object no longer accelerates and continues to fall at a constant speed.

8. How does the height from which an object falls influence the time it takes to reach the ground?

   תשובה: The time it takes for an object to reach the ground is proportional to the square root of the height from which it falls (assuming no air resistance). An object dropped from a greater height will take longer to reach the ground than one dropped from a shorter height.
9. What happens to the potential energy of an object as it falls freely under gravity?

   תשובה: As an object falls freely under gravity, its potential energy (relative to the ground) decreases. This decrease in potential energy is converted into kinetic energy, causing the object’s speed to increase.

10. If two objects of different shapes but the same mass are dropped from the same height in a vacuum, which will hit the ground first?

תשובה: In a vacuum, where there’s no air resistance, both objects will hit the ground at the same time. Their shape won’t matter because only gravity is acting on them, and their masses are the same.