Newton’s second law of motion – problems and solutions

Solved problems in Newton’s laws of motion – Newton’s second law of motion 

1. A 1 kg object accelerated at a constant 5 m/s². Estimate the net force needed to accelerate the object.

ידוע:

מסה (מ"ר) = 1 ק"ג

תְאוּצָה (a) = 5 m/s²

רצה : net force (∑F)

פתרון:

We use Newton’s second law to get the net force.

∑F = ma

∑F = (1 kg)(5 m/s²) = 5 ק"ג מטר לשנייה² = 5 ניוטון

2. מסה of an object = 1 kg, net force ∑F = 2 Newton. Determine the magnitude and direction of the object’s acceleration….

ידוע:

מסה (מ"ר) = 1 ק"ג

Net force (∑F) = 2 Newton

רצה : The magnitude and direction of the acceleration (a)

פתרון:

a = ∑F / m

א = 2 / 1

a = 2 מטר/שנייה²

The direction of the acceleration = the direction of the net force (∑F)

3. Object’s mass = 2 kg, F₁ = 5 Newton, F₂ = 3 Newton. The magnitude and direction of the acceleration is…

ידוע:

מסה (מ"ר) = 2 ק"ג

F₁ = 5 ניוטון

F₂ = 3 ניוטון

מבוקש: The magnitude and direction of the acceleration (a)

פתרון:

net force :

∑F = F₁ - פ₂ = 5 – 3 = 2 ניוטון

The magnitude of the acceleration :

a = ∑F / m

א = 2 / 2

a = 1 מטר/שנייה²

Direction of the acceleration = direction of the net force = direction of F₁

4. Object’s mass = 2 kg, F₁ = 10 Newton, F₂ = 1 Newton. The magnitude and direction of the acceleration is…

ידוע:

מסה (מ"ר) = 2 ק"ג

F₂ = 1 ניוטון

F₁ = 10 ניוטון

F_1x =F₁ cos 60^o = (10)(0.5) = 5 ניוטון

רצה : The magnitude and direction of the acceleration (a)

פתרון:

כוח נקי:

∑F = F_1x - פ₂ = 5 – 1 = 4 ניוטון

The magnitude of the acceleration :

a = ∑F / m

א = 4 / 2

a = 2 מטר/שנייה²

Direction of the acceleration = direction of the net force = direction of F_1x

5. F₁ = 10 Newton, F₂ = 1 Newton, m₁ = 1 ק"ג, מ"ר₂ = 2 kg. The magnitude and direction of the acceleration is…

ידוע:

Mass 1 (m₁) = 1 ק"ג

Mass 2 (m₂) = 2 ק"ג

F₁ = 10 ניוטון

F₂ = 1 ניוטון

רצה : The magnitude and direction of the acceleration (a)

פתרון:

The net force :

∑F = F₁ - פ₂ = 10 – 1 = 9 ניוטון

The magnitude of the acceleration :

a = ∑F / (m₁ + מ '₂)

a = 9 / (1 + 2)

א = 9 / 3

a = 3 מטר/שנייה²

The direction of the acceleration = the direction of the net force = direction of F₁

6.

A 40-kg block accelerated by a force of 200 N. Acceleration of the block is 3 m/s². Determine the magnitude of friction force experienced by the block.

א. 15 צפון

ב. 40 צפון

C. 43 צפון

ד. 80 צפון

ידוע:

מסה (מ"ר) = 40 ק"ג

כוח (F) = 200 ניוטון

תאוצה (a) = 3 מטר/שנייה²

מבוקש: כוח חיכוך (F_g)

פתרון:

המשוואה של חוק התנועה השני של ניוטון

∑F = ma

∑F = net force, m = mass, a = acceleration

The direction of force F rightward, the direction of friction force leftward (the direction of friction force is opposite with the direction of object’s motion).

Choose rightward as positive and leftward as negative.

∑F = ma

F – F_g = אמא

200 – ו_g = (40)(3)

200 – ו_g = 120

F_g = 200 - 120

F_g = 80 ניוטון

התשובה הנכונה היא ד.

7. Block A with a mass of 100-gram place above block B with a mass of 300 gram, and then block b pushed with a force of 5 N vertically upward. Determine the כוח נורמלי exerted by block B on block A.

א. 1 צפון

ב. 1.25 צפון

C. 2 צפון

ד. 3 צפון

ידוע:

כוח (F) = 5 ניוטון

מסת בלוק A (מ"ר_A) = 100 גרם = 0.1 ק"ג

מסת בלוק B (מ"ר)_B) = 300 גרם = 0.3 ק"ג

תאוצת הכבידה (גרם) = 10 מטר/שנייה²

מִשׁקָל of block A (w_A) = (0.1 ק"ג)(10 מטר/שנייה²) = 1 ק"ג מטר לשנייה² = 1 ניוטון

משקל בלוק B (משקל_B) = (0.3 ק"ג)(10 מטר/שנייה²) = 3 ק"ג מטר לשנייה² = 3 ניוטון

מבוקש: Normal force exerted by block B to block A

פתרון:

There are several forces that act on both block, as shown in figure.

F = push force (act on block B)

w_A = weight of block A (act on block A)

w_B = weight of block B (act on block B)

N_A = normal force exerted by block B on block A (Act on block A)

N_A’ = normal force exerted by block A on block B (Act on block B)

Apply Newton’s second law of motion on both blocks :

∑F = ma

פ – וו_A - w_B + N_A - N_A’ = (m_A + מ '_B) כדי

N_A וN_A’ are action-reaction forces that have the same magnitude but opposite in direction so eliminated from the equation.

פ – וו_A - w_B = (מ'_A + מ '_B) כדי

5 – 1 – 3 = (0.1 + 0.3) א

5 – 4 = (0.4) a

1 = (0.4) א

א = 1 / 0.4

a = 2.5 מטר/שנייה²

Apply Newton’s second law of motion on block A :

∑F = ma

N_A - w_A = מ_A a

N_A – 1 = (0.1)(2.5)

N_A - 1 = 0.25

N_A = 1 + 0.25

N_A = 1.25 ניוטון

התשובה הנכונה היא ב'.

8. An object with weight of 4 N supported by a cord and pulley. A force of 2 N acts on the block and one end of the cord pulled by a force of 9 N. Determine the net force acts on object X.

A. 3 N upward

B. 4 N downward

C. 9 N upward

D. 9 N downward

ידוע:

Weight of X (w_X) = 4 ניוטון

Pull force (F_x) = 2 ניוטון

Tension force (F_T) = 9 ניוטון

מבוקש: Net force acts on object X

פתרון:

Vertically upward forces that act on object X :

The tension force has the same magnitude in all part of the cord. So the tension force is 9 N.

Vertically downward forces that act on object X :

There are two forces that act on object X and both forces are vertically downward, the horizontal component of weight w_x and the horizontal component of force F_x.

Net force act on the object X :

F_T - w_X - פ_x = 9 – 4 – 2 = 9 – 6 = 3

The net force act on the object X is 3 Newton, vertically upward.

התשובה הנכונה היא A.

9. An object initially at rest on a smooth horizontal surface. A force of 16 N acts on the object so the object accelerated at 2 m/s². If the same object at rest on a rough horizontal surface so the friction force acts on the object is 2 N, then determine the acceleration of the object if the same force of 16 N acts on the object.

א. 1.75 מטר/שנייה²

ב. 1.50 מטר/שנייה²

כ-1.00 מטר/שנייה²

ד. 0.88 מטר/שנייה²

ידוע:

Force (F) = 16 Newton = 16 kg m/s²

תאוצה (a) = 2 מטר/שנייה²

Friction force (F_fric) = 2 Newton = 2 kg m/s²

מבוקש: Object’s acceleration ?

פתרון:

Smooth horizontal surface (no friction force) :

∑F = ma

F = ma

16 = (m) 2

m = 16/2

מטר = 8 ק"ג

Mass of object is 8 kilogram.

Rough horizontal surface (there is a friction force) :

∑F = ma

F – F_fric = אמא

16 – 2 = 8 a

14 = 8 א

א = 14 / 8

a = 1.75 מטר/שנייה²

Object’s acceleration is 1.75 m/s².

התשובה הנכונה היא A.

10. Tom and Andrew push an object on the smooth floor. Tom push the object with a force of 5.70 N. If the mass of the object is 2.00 kg and acceleration experienced by the object is 2.00 ms^-2, then determine the magnitude and direction of force act by Tom.

A. 1.70 N and its direction is opposite with force acted by Andre.w

B. 1.70 N and its direction same as force acted by Andrew

C. 2.30 N and its direction is opposite with force acted by Andrew.

D. 2.30 N and its direction same as force acted by Andrew.

ידוע:

Push force acted by Andrew (F₁) = 5.70 ניוטון

מסת העצם (מ') = 2.00 ק"ג

תאוצה (a) = 2.00 מטר/שנייה²

מבוקש: Magnitude and direction of force acted by Tom (F₂)

פתרון:

Apply Newton’s second law of motion :

∑F = ma

F₁ + ו₂ = אמא

5.70 + פ₂ = (2)(2)

5.70 + פ₂ = 4

F₂ = 4 - 5.70

F₂ = – 1.7 Newton

Minus sign indicated that (F₂) is opposite with push force act by Andrew (F₁).

התשובה הנכונה היא A.

11. If the mass of the block is the same, which figure shows the smallest acceleration?

פתרון

Net force A :

ΣF = 4 N + 2 N – 3 N = 6 N – 3 N = 3 Newton, leftward

Net force B :

ΣF = 2 N + 3 N – 4 N = 5 N – 4 N = 1 Newton, rightward

Net force C :

ΣF = 4 N + 3 N – 2 N = 7 N – 2 N = 5 Newton, rightward

Net force D :

ΣF = 3 N + 4 N + 2 N = 9 Newton, rightward

The equation of Newton’s second law :

ΣF = ma

a = ΣF / m

a = acceleration, ΣF = net force, m = mass

Based on the above formula, the acceleration (a) is directly proportional to the net force (ΣF) and inversely proportional to mass (m). If the mass of an object is the same, the greater the resultant force, the greater the acceleration or the smaller the resultant force, the smaller the acceleration.
Based on the above calculation, the smallest net force is 1 Newton so the acceleration is also smallest.

התשובה הנכונה היא ב'.

12. Some forces act on an object with a mass of 20 kg, as shown in the figure below.

Determine the object’s acceleration.

ידוע:

מסת העצם (מ') = 20 ק"ג

Net force (ΣF) = 25 N + 30 N – 15 N = 40 N

מבוקש: Acceleration of an object

פתרון:

Object’s acceleration calculated using the equation of Newton’s second law :

ΣF = ma

a = ΣF / m = 40 N / 20 kg = 2 N/kg = 2 m/s²

13. Which statements below describes Newton’s third law?

(1) Passengers pushed forward when the bus braked suddenly

(2) Books on paper are not falling when the paper is pulled quickly

(3) When playing skateboard when the foot pushes the ground back then the skateboard will slide forward

(4) הוars pushed backward, boats moving forward

פתרון:

(1) החוק הראשון של ניוטון

(2) Newton’s first law

(3) Newton’s third law

(4) Newton’s third law

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1. מסה ומשקל
2. כוח רגיל
3. חוק התנועה השני של ניוטון
4. כוח חיכוך
5. תנועה על משטח אופקי ללא כוח חיכוך
6. תנועתם של שני גופים בעלי תאוצה זהה על משטח אופקי מחוספס עם כוח חיכוך
7. תנועה על מישור משופע ללא כוח חיכוך
8. תנועה על מישור משופע גס עם כוח החיכוך
9. תנועה במעלית
10. תנועת הגופים מחוברת באמצעות חוטים וגלגלות
11. שני גופים בעלי גודל תאוצה זהה
12. עיגול עקומה שטוחה - דינמיקה של תנועה מעגלית
13. עיגול עקומה משופעת - דינמיקה של תנועה מעגלית
14. תנועה אחידה במעגל אופקי
15. כוח צנטריפטלי בתנועה מעגלית אחידה