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GRADE 9 PRACTICE

Physics Problems: Newton's laws, Grade 9

Inertial systems, forces, gravity, weight and friction.

18 problems across 4 sub-topics
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Problem statements

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18 problems
Position in this set: 1 from 18

Problem #10

Newton's three laws

What concept does the description correspond to: “The acceleration of a body is determined by the vector sum of forces and is inversely proportional to the mass.”?

Answer options

  1. \text{Newton's second law}
  2. \text{Inertial reference frame}
  3. \text{Newton's third law}
  4. \text{Point particle}
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Given
\text{Description}
\text{An object's acceleration is determined by the vector sum of the forces on it and is inversely proportional to its mass.}
Find

\text{name concepts}

  1. \text{Let's compare approval with definition}

    First add all the forces as vectors. Then relate each component of the net force to the corresponding component of acceleration.

  2. \text{Let's formulate conclusion}\text{Concept} = \text{Newton's second law}

Answer\text{Concept} = \text{Newton's second law}

Position in this set: 2 from 18

Problem #11

Newton's three laws

What concept does the description correspond to: “A system in which a free body remains at rest or in uniform linear motion.”?

Answer options

  1. \text{Inertial reference frame}
  2. \text{Newton's second law}
  3. \text{Newton's third law}
  4. \text{Point particle}
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Given
\text{Description}
\text{A frame in which a free object remains at rest or moves in a straight line at constant velocity.}
Find

\text{name concepts}

  1. \text{Let's compare approval with definition}

    In school mechanics, a frame moving at constant velocity relative to an inertial frame is also inertial.

  2. \text{Let's formulate conclusion}\text{Concept} = \text{Inertial reference frame}

Answer\text{Concept} = \text{Inertial reference frame}

Position in this set: 3 from 18

Problem #12

Newton's laws

A body of mass 3 kg is acted upon by a constant resultant force of 12 N. Find the acceleration.

Answer options

  1. 4\,\text{м/с}^{2}
  2. 0{,}25\,\text{м/с}^{2}
  3. 9\,\text{м/с}^{2}
  4. 36\,\text{м/с}^{2}
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Given
m
3\,\text{кг}
F
12\,\text{Н}
Find

a

  1. F=ma
  2. a=\frac{F}{m}a=\frac{12}{3}\,\text{м/с}^{2}a = 4\,\text{м/с}^{2}

Answer4\,\text{м/с}^{2}

Position in this set: 4 from 18

Problem #13

Gravity, elasticity, weight and friction

What concept corresponds to the description: “Any two bodies attract with a force depending on the masses and the distance between them.”?

Answer options

  1. \text{Universal gravitation}
  2. \text{Weight, increased apparent weight and weightlessness}
  3. \text{Elasticity and friction}
  4. \text{Point particle}
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Given
\text{Description}
\text{Any two bodies attract one another with a force that depends on their masses and the distance between them.}
Find

\text{name concepts}

  1. \text{Let's compare approval with definition}

    For spheres, measure the distance between their centres. The acceleration g depends on the celestial body's mass and radius, so it differs on other planets.

  2. \text{Let's formulate conclusion}\text{Concept} = \text{Universal gravitation}

Answer\text{Concept} = \text{Universal gravitation}

Position in this set: 5 from 18

Problem #14

Gravity, elasticity, weight and friction

What concept does the description correspond to: “Weight depends on the acceleration of the support: with upward acceleration it increases, and with free fall it becomes zero.”?

Answer options

  1. \text{Weight, increased apparent weight and weightlessness}
  2. \text{Universal gravitation}
  3. \text{Elasticity and friction}
  4. \text{Point particle}
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Given
\text{Description}
\text{Weight depends on the support's acceleration: it increases during upward acceleration and becomes zero during free fall.}
Find

\text{name concepts}

  1. \text{Let's compare approval with definition}

    Weightlessness does not mean that gravitation disappears: the body and its support simply fall with the same acceleration.

  2. \text{Let's formulate conclusion}\text{Concept} = \text{Weight, increased apparent weight and weightlessness}

Answer\text{Concept} = \text{Weight, increased apparent weight and weightlessness}

Position in this set: 6 from 18

Problem #15

Elastic restoring force

A spring with a stiffness of 250 N/m lengthens by 4 cm. Find the modulus of the elastic force.

Answer options

  1. 10\,\text{Н}
  2. 0{,}1\,\text{Н}
  3. 6{,}25\,\text{Н}
  4. 1000\,\text{Н}
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Given
k
250\,\text{Н/м}
\Delta l
4\,\text{см}0{,}04\,\text{м}
Find

F_{\text{упр}}

  1. F_{\text{упр}}=k\Delta lF_{\text{упр}}=250\cdot0{,}04\,\text{Н}F_{\text{упр}} = 10\,\text{Н}

Answer10\,\text{Н}

Position in this set: 7 from 18

Problem #82

Newton's three laws

Resultant force on a body of mass 4 kg is equal to 12 H. Find the acceleration.

Answer options

  1. 3\,\text{м/с}^{2}
  2. 6\,\text{м/с}^{2}
  3. 1{,}5\,\text{м/с}^{2}
  4. 9\,\text{м/с}^{2}
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Given
m
4\,\text{кг}
F
12\,\text{Н}
Find

a

  1. a=\frac{F}{m}a=\frac{12}{4}a=3\,\text{м/с}^{2}

    We divide the resultant force, not the individual force, by the mass.

Answer3\,\text{м/с}^{2}

Position in this set: 8 from 18

Problem #83

Newton's three laws

Resultant force on a body of mass 5 kg is equal to 20 H. Find the acceleration.

Answer options

  1. 8\,\text{м/с}^{2}
  2. 4\,\text{м/с}^{2}
  3. 2\,\text{м/с}^{2}
  4. 12\,\text{м/с}^{2}
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Given
m
5\,\text{кг}
F
20\,\text{Н}
Find

a

  1. a=\frac{F}{m}a=\frac{20}{5}a=4\,\text{м/с}^{2}

    We divide the resultant force, not the individual force, by the mass.

Answer4\,\text{м/с}^{2}

Position in this set: 9 from 18

Problem #84

Newton's three laws

Body mass 3 kg is pulled to the right by force 20 N, the resistance force to the left is 5 H. Find the acceleration module.

Answer options

  1. 10\,\text{м/с}^{2}
  2. 5\,\text{м/с}^{2}
  3. 2{,}5\,\text{м/с}^{2}
  4. 15\,\text{м/с}^{2}
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Given
m
3\,\text{кг}
F_1
20\,\text{Н}
F_2
5\,\text{Н}
Find

a

  1. F=F_1-F_2F=20 - 5F=15\,\text{Н}

    We choose the positive direction to the right.

  2. a=\frac{F}{m}a=\frac{15}{3}a=5\,\text{м/с}^{2}

    We apply Newton's law to the resultant.

Answer5\,\text{м/с}^{2}

Position in this set: 10 from 18

Problem #85

Newton's three laws

Body mass 4 kg is pulled to the right by force 30 N, the resistance force to the left is 6 H. Find the acceleration module.

Answer options

  1. 12\,\text{м/с}^{2}
  2. 3\,\text{м/с}^{2}
  3. 6\,\text{м/с}^{2}
  4. 18\,\text{м/с}^{2}
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Given
m
4\,\text{кг}
F_1
30\,\text{Н}
F_2
6\,\text{Н}
Find

a

  1. F=F_1-F_2F=30 - 6F=24\,\text{Н}

    We choose the positive direction to the right.

  2. a=\frac{F}{m}a=\frac{24}{4}a=6\,\text{м/с}^{2}

    We apply Newton's law to the resultant.

Answer6\,\text{м/с}^{2}

Position in this set: 11 from 18

Problem #86

Newton's three laws

Body mass 2 kg was at rest. A constant horizontal force was applied to it 14 N at constant resistance force 4 N. Find a way behind 4 s.

Answer options

  1. 80\,\text{м}
  2. 20\,\text{м}
  3. 40\,\text{м}
  4. 120\,\text{м}
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Given
m
2\,\text{кг}
F
14\,\text{Н}
R
4\,\text{Н}
t
4\,\text{с}
Find

S

  1. F_{\text{рез}}=F-RF_{\text{рез}}=14 - 4F_{\text{рез}}=10\,\text{Н}

    Subtract the opposing force.

  2. a=\frac{F_{\text{рез}}}{m}a=\frac{10}{2}a=5\,\text{м/с}^{2}

    Mass relates force and acceleration.

  3. S=\frac{at^2}{2}S=\frac{5 \cdot {4}^{2}}{2}S=40\,\text{м}

    The initial speed is zero, the acceleration is constant.

Answer40\,\text{м}

Position in this set: 12 from 18

Problem #87

Newton's three laws

Body mass 3 kg was at rest. A constant horizontal force was applied to it 21 N at constant resistance force 9 N. Find a way behind 5 s.

Answer options

  1. 100\,\text{м}
  2. 25\,\text{м}
  3. 150\,\text{м}
  4. 50\,\text{м}
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Given
m
3\,\text{кг}
F
21\,\text{Н}
R
9\,\text{Н}
t
5\,\text{с}
Find

S

  1. F_{\text{рез}}=F-RF_{\text{рез}}=21 - 9F_{\text{рез}}=12\,\text{Н}

    Subtract the opposing force.

  2. a=\frac{F_{\text{рез}}}{m}a=\frac{12}{3}a=4\,\text{м/с}^{2}

    Mass relates force and acceleration.

  3. S=\frac{at^2}{2}S=\frac{4 \cdot {5}^{2}}{2}S=50\,\text{м}

    The initial speed is zero, the acceleration is constant.

Answer50\,\text{м}

Position in this set: 13 from 18

Problem #88

Gravity, elasticity, weight and friction

Body mass 4 kg slides horizontally. Friction coefficient 0{,}2, g = 10 m/s². Find the friction force if there are no other vertical forces.

Answer options

  1. 16\,\text{Н}
  2. 8\,\text{Н}
  3. 4\,\text{Н}
  4. 24\,\text{Н}
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Given
m
4\,\text{кг}
u
0{,}2\,\text{безразм.}
g
10\,\text{м/с}^{2}
Find

F_{\text{тр}}

  1. F_{\text{тр}}=\mu mgF_{\text{тр}}=0{,}2 \cdot 4 \cdot 10F_{\text{тр}}=8\,\text{Н}

    The normal reaction is mg.

Answer8\,\text{Н}

Position in this set: 14 from 18

Problem #89

Gravity, elasticity, weight and friction

Body mass 6 kg slides horizontally. Friction coefficient 0{,}3, g = 10 m/s². Find the friction force if there are no other vertical forces.

Answer options

  1. 36\,\text{Н}
  2. 9\,\text{Н}
  3. 18\,\text{Н}
  4. 54\,\text{Н}
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Given
m
6\,\text{кг}
u
0{,}3\,\text{безразм.}
g
10\,\text{м/с}^{2}
Find

F_{\text{тр}}

  1. F_{\text{тр}}=\mu mgF_{\text{тр}}=0{,}3 \cdot 6 \cdot 10F_{\text{тр}}=18\,\text{Н}

    The normal reaction is mg.

Answer18\,\text{Н}

Position in this set: 15 from 18

Problem #90

Gravity, elasticity, weight and friction

The elevator accelerates up with acceleration 2 m/s². Passenger weight 60 kg, g = 10 m/s². Find the weight of the passenger.

Answer options

  1. 1440\,\text{Н}
  2. 360\,\text{Н}
  3. 720\,\text{Н}
  4. 2160\,\text{Н}
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Given
a
2\,\text{м/с}^{2}
m
60\,\text{кг}
g
10\,\text{м/с}^{2}
Find

P

  1. F=maF=60 \cdot 2F=120\,\text{Н}

    The resultant is directed upward.

  2. P=mg+maP=60 \cdot 10 + 120P=720\,\text{Н}

    The support reaction exceeds the force of gravity by ma.

Answer720\,\text{Н}

Position in this set: 16 from 18

Problem #91

Gravity, elasticity, weight and friction

The elevator accelerates up with acceleration 3 m/s². Passenger weight 70 kg, g = 10 m/s². Find the weight of the passenger.

Answer options

  1. 1820\,\text{Н}
  2. 455\,\text{Н}
  3. 2730\,\text{Н}
  4. 910\,\text{Н}
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Given
a
3\,\text{м/с}^{2}
m
70\,\text{кг}
g
10\,\text{м/с}^{2}
Find

P

  1. F=maF=70 \cdot 3F=210\,\text{Н}

    The resultant is directed upward.

  2. P=mg+maP=70 \cdot 10 + 210P=910\,\text{Н}

    The support reaction exceeds the force of gravity by ma.

Answer910\,\text{Н}

Position in this set: 17 from 18

Problem #92

Gravity, elasticity, weight and friction

Spring stiffness 200 N/m stretched by 0{,}1 m and pulls horizontally on a block of mass 2 kg, sliding in the direction of the spring force. The friction coefficient is 0{,}2, g = 10 m/s². Find the acceleration at this moment.

Answer options

  1. 16\,\text{м/с}^{2}
  2. 4\,\text{м/с}^{2}
  3. 24\,\text{м/с}^{2}
  4. 8\,\text{м/с}^{2}
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Given
k
200\,\text{Н/м}
x
0{,}1\,\text{м}
m
2\,\text{кг}
u
0{,}2\,\text{безразм.}
g
10\,\text{м/с}^{2}
Find

a

  1. F=kxF=200 \cdot 0{,}1F=20\,\text{Н}

    The elastic force at the moment under consideration.

  2. R=\mu mgR=0{,}2 \cdot 2 \cdot 10R=4\,\text{Н}

    Friction is directed against sliding.

  3. a=\frac{F-R}{m}a=\frac{(20 - 4)}{2}a=8\,\text{м/с}^{2}

    We find the instantaneous acceleration using the resultant.

Answer8\,\text{м/с}^{2}

Position in this set: 18 from 18

Problem #93

Gravity, elasticity, weight and friction

Spring stiffness 300 N/m stretched by 0{,}12 m and pulls horizontally on a block of mass 3 kg, sliding in the direction of the spring force. The friction coefficient is 0{,}2, g = 10 m/s². Find the acceleration at this moment.

Answer options

  1. 10\,\text{м/с}^{2}
  2. 20\,\text{м/с}^{2}
  3. 5\,\text{м/с}^{2}
  4. 30\,\text{м/с}^{2}
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Given
k
300\,\text{Н/м}
x
0{,}12\,\text{м}
m
3\,\text{кг}
u
0{,}2\,\text{безразм.}
g
10\,\text{м/с}^{2}
Find

a

  1. F=kxF=300 \cdot 0{,}12F=36\,\text{Н}

    The elastic force at the moment under consideration.

  2. R=\mu mgR=0{,}2 \cdot 3 \cdot 10R=6\,\text{Н}

    Friction is directed against sliding.

  3. a=\frac{F-R}{m}a=\frac{(36 - 6)}{3}a=10\,\text{м/с}^{2}

    We find the instantaneous acceleration using the resultant.

Answer10\,\text{м/с}^{2}

The theory behind these problems

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Newton's three lawsInertial frames, net force and interaction pairs.Gravity, elasticity, weight and frictionUniversal gravitation, Hooke's law, increased apparent weight and weightlessness.

Formulas by topic

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Apparent weight (force on a support)P · НSpring constantk · Н/мMassm · кгForceF · НExtensionΔl · м