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Question Bank: Displacement and Force in Two Dimensions
\[1\star\]
One of the following physical quantities is a scalar quantity
Acceleration -C
Force -A
Velocity -D
Distance -B
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Choose the correct answer
\[2\star\]
Force is considered a vector physical quantity and is determined
by knowing
Its unit of measurement -C
Its direction only -A
Its magnitude and direction -D
Its magnitude only -B
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Choose the correct answer
\[3\star\]
In the grid below, there is a set of vectors
with real dimensions. One of the following statements is correct
\[\vec A=\vec D \;\;\;\;\;\;-C\]
\[\vec A=\vec E\;\;\;\;\;\;-A\]
\[\vec F=\vec B\;\;\;\;\;\;-D\]
\[ \vec C=\vec B\;\;\;\;\;\;-B\]
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\[4\star\]
Four vectors
\[A,B,C,D\] their magnitudes and directions are shown in the figure below
Which of the following methods shows the resultant vector graphically
\[\vec A +\vec B+\vec C+\vec D= ?\]
Figure 3 -C
Figure 1 -A
All of the above -D
Figure 2 -B
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\[5\star\star\]
A box is affected by two forces \[F_1=50 N\] eastward and \[F_2=30 N\] northward. The resultant force on the box equals:
\[ F(net)=65.4 N \;\;\;,\;\;\; 𝜃=69.9^0 \;\;\;\;\;\;-C\]
East of North
\[ F(net)=80 N\;\;\; ,\;\;\; 𝜃=20^0 \;\;\;\;\;\;-A\]
North of East
\[F(net)=75.2 N \;\;\;,\;\;\; 𝜃=33.8^0\;\;\;\;\;\;-D\]
East of North
\[ F(net)=58.3 N \;\;\;,\;\;\; 𝜃=30.9^0\;\;\;\;\;\;-B\]
North of East
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\[6\star\]
Two vectors, the magnitude of each is the length of the vector and the direction of each is shown in the figure below
One of the following answers correctly represents the resultant of the two vectors
Figure 3
-C
Figure 1
-A
Figure 4
-D
Figure 2
-B
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Choose the correct answer
\[7\star\star\]
Ahmed moved west a distance of
\[60\;m\] then changed direction and moved a distance of
\[80\;m\] south. The resultant displacement equals
\[ R=140 m \;\;\;,\;\;\; 𝜃=35.3^0 \;\;\;\;\;\;-C\]
South West
\[ R=110 m\;\;\; ,\;\;\; 𝜃=53.1^0 \;\;\;\;\;\;-A\]
West South
\[R=100 m \;\;\;,\;\;\; 𝜃=53.1^0\;\;\;\;\;\;-D\]
South West
\[ R=120 m \;\;\;,\;\;\; 𝜃=53.1^0\;\;\;\;\;\;-B\]
West South
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\[8\star\star\]
Majid moved east a distance of
\[50\;m\] then changed direction and moved south a distance of
\[40\;m\]. Find the resultant displacement
\[ X=64 m \;\;\;,\;\;\; 𝜃=38.66^0 \;\;\;\;\;\;-C\]
South East
\[ X=77 m\;\;\; ,\;\;\; 𝜃=51.33^0 \;\;\;\;\;\;-A\]
East South
\[X=90 m \;\;\;,\;\;\; 𝜃=38.66^0\;\;\;\;\;\;-D\]
East South
\[ X=73 m \;\;\;,\;\;\; 𝜃=45.46^0\;\;\;\;\;\;-B\]
South East
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\[9\star\star \star\]
In the figure below we have two displacements \[\vec A=3 m , \vec B=5 m\] and the vector
\[B\] makes an angle of \[𝜃=53.1^0\] with the positive
\[X\] axis. Find the resultant displacement \[\vec R=\vec A +\vec B\] and determine the angle between the resultant and the vector
\[\vec A\]
\[ R=9.1 m \;\;\;,\;\;\; 𝛼=14.8^0 \;\;\;\;\;\;-C\]
\[ R=7.2 m\;\;\; ,\;\;\; 𝛼=19.5^0 \;\;\;\;\;\;-A\]
\[R=11.4 m \;\;\;,\;\;\; 𝛼=23.1^0\;\;\;\;\;\;-D\]
\[ R=8.4 m \;\;\;,\;\;\; 𝛼=24.3^0\;\;\;\;\;\;-B\]
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\[10\star\]
A force vector
\[F=60\;\; N\]
makes an angle of \[𝜃=30^0\]
south of west. The components of the force on the perpendicular axes equal
\[ FX=41.58 N \;\;\;,\;\;\; FY= 54.3 N \;\;\;\;\;\;-C\]
\[ FX=-51.96 N\;\;\; ,\;\;\; FY= -30 N \;\;\;\;\;\;-A\]
\[ FX=-42.64 N \;\;\;,\;\;\; FY= 40.7 N\;\;\;\;\;\;-D\]
\[ FX=-45.36 N \;\;\;,\;\;\; FY= -18.2 N\;\;\;\;\;\;-B\]
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\[11\star\]
Three vectors as in the figure. One of the following statements is correct
\[ \vec B=\vec C+ \vec A \;\;\;\;\;\;-C\]
\[ \vec A=\vec C+ \vec B \;\;\;\;\;\;-A\]
\[ \vec A+ \vec C+ \vec B=0\;\;\;\;\;\;-D\]
\[ \vec C=\vec A+ \vec B\;\;\;\;\;\;-B\]
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\[12\star\]
Three vectors as in the figure. One of the following statements is correct
\[ \vec B=\vec C+ \vec A \;\;\;\;\;\;-C\]
\[ \vec A=\vec C+ \vec B \;\;\;\;\;\;-A\]
\[ \vec A+ \vec C+ \vec B=0\;\;\;\;\;\;-D\]
\[ \vec C=\vec A+ \vec B\;\;\;\;\;\;-B\]
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\[13\star\]
Two vectors, the first has a magnitude of 15 and the second has a magnitude of 10. Which of the following answers cannot be the resultant of the two vectors?
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\[R=20 \;\;\;\;\;\;-C\]
\[ R=4\;\;\;\;\;\;-A\]
\[ R=25\;\;\;\;\;\;-D\]
\[ R=5\;\;\;\;\;\;-B\]
\[14\star\star\star\]
A triangle of vectors as shown in the figure with vector magnitudes shown below. The angle \[𝜃 =?\] equals
\[𝜃=130^0 \;\;\;\;\;\;-C\]
\[𝜃=140 ^0\;\;\;\;\;\;-A\]
\[ 𝜃=120^0\;\;\;\;\;\;-D\]
\[ 𝜃=110^0\;\;\;\;\;\;-B\]
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\[15\star\]
A vector is resolved into two components as shown in the figure below
The values of the components are
\[A_X=6 , A_Y=5\]
The magnitude of the vector equals
\[A =7.8\;\;\;\;\;\;-C\]
\[A =8.9 \;\;\;\;\;\;-A\]
\[ A =10.2 \;\;\;\;\;\;-D\]
\[ A =11 \;\;\;\;\;\;-B\]
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\[16\star\]
Four vectors
\[A,B,C,D\]
are located on the grid below
When one of the vectors is analyzed
its vertical component on the
\[Y\]
axis is zero
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Choose the correct answer
\[17\star\star\]
Two forces acted on an object
The components of each force are shown in
the figure below
Using the figure
the resultant of the two forces and the direction
of the resultant equals
\[ F(net)=9.5 N \;\;\;,\;\;\; 𝜃=71.6^0 \;\;\;\;\;\;-C\]
\[ F(net)=6.3 N\;\;\; ,\;\;\; 𝜃=54.2^0 \;\;\;\;\;\;-A\]
\[F(net)=10.8 N \;\;\;,\;\;\; 𝜃=38.8^0\;\;\;\;\;\;-D\]
\[ F(net)=8.4 N \;\;\;,\;\;\; 𝜃=28.4^0\;\;\;\;\;\;-B\]
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\[18\star\]
Two forces, each with magnitude
\[50\;N\]
acted on a box in different ways
Arrange the magnitude of the resultant force from smallest to largest
\[ B> C> D >A \;\;\;\;\;\;-C\]
\[ C > B> A >D \;\;\;\;\;\;-A\]
\[ A > D> B >C \;\;\;\;\;\;-D\]
\[ A >C> B >D \;\;\;\;\;\;-B\]
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\[19\star\star \star\]
A student started from school towards the east and covered a distance of
\[120\;m\]
then changed direction and deviated at an angle of 40 degrees northeast and covered a distance of
\[90\;m\] until he reached home. The displacement covered equals
\[ d=197.6 m \;\;\;, \;\;\;𝜃=17^0 \;\;\;\;\;\;-C\]
Northeast
\[d=210 m \;\;\;, \;\;\;𝜃=35^0 \;\;\;\;\;\;-A\]
Northeast
\[ d=167.3 m \;\;\;, \;\;\;𝜃=45^0\;\;\;\;\;\;-D\]
East North
\[ d=157.8 m \;\;\;, \;\;\;𝜃=23^0\;\;\;\;\;\;-B\]
East North
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\[20\star\star \]
A wooden cube with mass
\[30 kg\]
placed on a rough horizontal surface
A force inclined above the horizontal
at an angle of 30 degrees
and with magnitude 400 Newtons was applied. The value of the normal force equals
\[FN = 157.4\;\; N \;\;\;\;\;\;-C\]
\[FN = 294.3\;\; N \;\;\;\;\;\;-A\]
\[ FN = 135.4 \;\;N \;\;\;\;\;\;-D\]
\[ FN = 94.3\;\; N \;\;\;\;\;\;-B\]
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\[21\star\star \]
In the figure below, an object is placed on a rough horizontal plane
A pulling force of 20 Newtons is applied to it at an angle of 30 degrees above the horizontal
The object moves, so the resultant force on the
\[X\] axis equals
\[∑𝐹𝑋=7.3\;\; N \;\;\;\;\;\;-C\]
\[∑𝐹𝑋=10\;\; N \;\;\;\;\;\;-A\]
\[ ∑𝐹𝑋=9.6\;\;N \;\;\;\;\;\;-D\]
\[ ∑𝐹𝑋=2.4\;\; N \;\;\;\;\;\;-B\]
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Choose the correct answer
\[22\star\star \]
In the figure below, an object weighing 26 Newtons is placed on a rough horizontal plane
A pulling force of 20 Newtons is applied to it at an angle of 30 degrees above the horizontal
The object moves. If the kinetic friction force is 10 Newtons, then the coefficient of kinetic friction
equals
\[ 𝜇K = 0.542 \;\;\;\;\;\;-C\]
\[ 𝜇K = 0.43 \;\;\;\;\;\;-A\]
\[ 𝜇K = 0.384 \;\;\;\;\;\;-D\]
\[ 𝜇K = 0.625\;\;\;\;\;\;-B\]
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Choose the correct answer
\[23\star\star \]
Three concurrent forces acted on an object as shown in the figure below
The resultant force
on the horizontal axis and on the vertical axis equals
\[ FX=91.2 N \;\;\;,\;\;\; FY= 40 N \;\;\;\;\;\;-C\]
\[ FX=-131.2 N\;\;\; ,\;\;\; FY= -10 N \;\;\;\;\;\;-A\]
\[ FX=-0 N \;\;\;,\;\;\; FY= 0 N\;\;\;\;\;\;-D\]
\[ FX=11.2 N \;\;\;,\;\;\; FY= -40 N\;\;\;\;\;\;-B\]
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Question Bank: Displacement and Force in Two Dimensions |
One of the following physical quantities is a scalar quantity
Acceleration -C |
Force -A |
Velocity -D |
Distance -B |
Click here to show the solution
Choose the correct answer
Force is considered a vector physical quantity and is determined by knowing
Its unit of measurement -C |
Its direction only -A |
Its magnitude and direction -D |
Its magnitude only -B |
Click here to show the solution
Choose the correct answer
In the grid below, there is a set of vectors
with real dimensions. One of the following statements is correct
\[\vec A=\vec D \;\;\;\;\;\;-C\] |
\[\vec A=\vec E\;\;\;\;\;\;-A\] |
\[\vec F=\vec B\;\;\;\;\;\;-D\] |
\[ \vec C=\vec B\;\;\;\;\;\;-B\] |
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Choose the correct answer
Four vectors
\[A,B,C,D\] their magnitudes and directions are shown in the figure below
Which of the following methods shows the resultant vector graphically
\[\vec A +\vec B+\vec C+\vec D= ?\]
Figure 3 -C |
Figure 1 -A |
All of the above -D |
Figure 2 -B |
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Choose the correct answer
A box is affected by two forces \[F_1=50 N\] eastward and \[F_2=30 N\] northward. The resultant force on the box equals:
\[ F(net)=65.4 N \;\;\;,\;\;\; 𝜃=69.9^0 \;\;\;\;\;\;-C\] East of North |
\[ F(net)=80 N\;\;\; ,\;\;\; 𝜃=20^0 \;\;\;\;\;\;-A\] North of East |
\[F(net)=75.2 N \;\;\;,\;\;\; 𝜃=33.8^0\;\;\;\;\;\;-D\] East of North |
\[ F(net)=58.3 N \;\;\;,\;\;\; 𝜃=30.9^0\;\;\;\;\;\;-B\] North of East |
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Two vectors, the magnitude of each is the length of the vector and the direction of each is shown in the figure below
One of the following answers correctly represents the resultant of the two vectors
Figure 3 -C |
Figure 1 -A |
Figure 4 -D |
Figure 2 -B |
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Choose the correct answer
Ahmed moved west a distance of \[60\;m\] then changed direction and moved a distance of \[80\;m\] south. The resultant displacement equals
\[ R=140 m \;\;\;,\;\;\; 𝜃=35.3^0 \;\;\;\;\;\;-C\] South West |
\[ R=110 m\;\;\; ,\;\;\; 𝜃=53.1^0 \;\;\;\;\;\;-A\] West South |
\[R=100 m \;\;\;,\;\;\; 𝜃=53.1^0\;\;\;\;\;\;-D\] South West |
\[ R=120 m \;\;\;,\;\;\; 𝜃=53.1^0\;\;\;\;\;\;-B\] West South |
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Majid moved east a distance of
\[50\;m\] then changed direction and moved south a distance of
\[40\;m\]. Find the resultant displacement
\[ X=64 m \;\;\;,\;\;\; 𝜃=38.66^0 \;\;\;\;\;\;-C\] South East |
\[ X=77 m\;\;\; ,\;\;\; 𝜃=51.33^0 \;\;\;\;\;\;-A\] East South |
\[X=90 m \;\;\;,\;\;\; 𝜃=38.66^0\;\;\;\;\;\;-D\] East South |
\[ X=73 m \;\;\;,\;\;\; 𝜃=45.46^0\;\;\;\;\;\;-B\] South East |
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In the figure below we have two displacements \[\vec A=3 m , \vec B=5 m\] and the vector
\[B\] makes an angle of \[𝜃=53.1^0\] with the positive
\[X\] axis. Find the resultant displacement \[\vec R=\vec A +\vec B\] and determine the angle between the resultant and the vector
\[\vec A\]
\[ R=9.1 m \;\;\;,\;\;\; 𝛼=14.8^0 \;\;\;\;\;\;-C\] |
\[ R=7.2 m\;\;\; ,\;\;\; 𝛼=19.5^0 \;\;\;\;\;\;-A\] |
\[R=11.4 m \;\;\;,\;\;\; 𝛼=23.1^0\;\;\;\;\;\;-D\] |
\[ R=8.4 m \;\;\;,\;\;\; 𝛼=24.3^0\;\;\;\;\;\;-B\] |
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A force vector \[F=60\;\; N\] makes an angle of \[𝜃=30^0\] south of west. The components of the force on the perpendicular axes equal
\[ FX=41.58 N \;\;\;,\;\;\; FY= 54.3 N \;\;\;\;\;\;-C\] |
\[ FX=-51.96 N\;\;\; ,\;\;\; FY= -30 N \;\;\;\;\;\;-A\] |
\[ FX=-42.64 N \;\;\;,\;\;\; FY= 40.7 N\;\;\;\;\;\;-D\] |
\[ FX=-45.36 N \;\;\;,\;\;\; FY= -18.2 N\;\;\;\;\;\;-B\] |
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Three vectors as in the figure. One of the following statements is correct
\[ \vec B=\vec C+ \vec A \;\;\;\;\;\;-C\] |
\[ \vec A=\vec C+ \vec B \;\;\;\;\;\;-A\] |
\[ \vec A+ \vec C+ \vec B=0\;\;\;\;\;\;-D\] |
\[ \vec C=\vec A+ \vec B\;\;\;\;\;\;-B\] |
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Three vectors as in the figure. One of the following statements is correct
\[ \vec B=\vec C+ \vec A \;\;\;\;\;\;-C\] |
\[ \vec A=\vec C+ \vec B \;\;\;\;\;\;-A\] |
\[ \vec A+ \vec C+ \vec B=0\;\;\;\;\;\;-D\] |
\[ \vec C=\vec A+ \vec B\;\;\;\;\;\;-B\] |
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Two vectors, the first has a magnitude of 15 and the second has a magnitude of 10. Which of the following answers cannot be the resultant of the two vectors?
Click here to show solution
\[R=20 \;\;\;\;\;\;-C\] |
\[ R=4\;\;\;\;\;\;-A\] |
\[ R=25\;\;\;\;\;\;-D\] |
\[ R=5\;\;\;\;\;\;-B\] |
A triangle of vectors as shown in the figure with vector magnitudes shown below. The angle \[𝜃 =?\] equals
\[𝜃=130^0 \;\;\;\;\;\;-C\] |
\[𝜃=140 ^0\;\;\;\;\;\;-A\] |
\[ 𝜃=120^0\;\;\;\;\;\;-D\] |
\[ 𝜃=110^0\;\;\;\;\;\;-B\] |
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A vector is resolved into two components as shown in the figure below The values of the components are \[A_X=6 , A_Y=5\] The magnitude of the vector equals
\[A =7.8\;\;\;\;\;\;-C\] |
\[A =8.9 \;\;\;\;\;\;-A\] |
\[ A =10.2 \;\;\;\;\;\;-D\] |
\[ A =11 \;\;\;\;\;\;-B\] |
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Choose the correct answer
Four vectors
\[A,B,C,D\]
are located on the grid below
When one of the vectors is analyzed
its vertical component on the
\[Y\]
axis is zero
Click here to show solution method
Choose the correct answer
Two forces acted on an object The components of each force are shown in the figure below Using the figure the resultant of the two forces and the direction of the resultant equals
\[ F(net)=9.5 N \;\;\;,\;\;\; 𝜃=71.6^0 \;\;\;\;\;\;-C\] |
\[ F(net)=6.3 N\;\;\; ,\;\;\; 𝜃=54.2^0 \;\;\;\;\;\;-A\] |
\[F(net)=10.8 N \;\;\;,\;\;\; 𝜃=38.8^0\;\;\;\;\;\;-D\] |
\[ F(net)=8.4 N \;\;\;,\;\;\; 𝜃=28.4^0\;\;\;\;\;\;-B\] |
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Choose the correct answer
Two forces, each with magnitude
\[50\;N\]
acted on a box in different ways
Arrange the magnitude of the resultant force from smallest to largest
\[ B> C> D >A \;\;\;\;\;\;-C\] |
\[ C > B> A >D \;\;\;\;\;\;-A\] |
\[ A > D> B >C \;\;\;\;\;\;-D\] |
\[ A >C> B >D \;\;\;\;\;\;-B\] |
Click here to show solutionChoose the correct answer
A student started from school towards the east and covered a distance of \[120\;m\] then changed direction and deviated at an angle of 40 degrees northeast and covered a distance of \[90\;m\] until he reached home. The displacement covered equals
\[ d=197.6 m \;\;\;, \;\;\;𝜃=17^0 \;\;\;\;\;\;-C\] Northeast |
\[d=210 m \;\;\;, \;\;\;𝜃=35^0 \;\;\;\;\;\;-A\] Northeast |
\[ d=167.3 m \;\;\;, \;\;\;𝜃=45^0\;\;\;\;\;\;-D\] East North |
\[ d=157.8 m \;\;\;, \;\;\;𝜃=23^0\;\;\;\;\;\;-B\] East North |
Click here to show solutionChoose the correct answer
A wooden cube with mass
\[30 kg\]
placed on a rough horizontal surface
A force inclined above the horizontal
at an angle of 30 degrees
and with magnitude 400 Newtons was applied. The value of the normal force equals
\[FN = 157.4\;\; N \;\;\;\;\;\;-C\] |
\[FN = 294.3\;\; N \;\;\;\;\;\;-A\] |
\[ FN = 135.4 \;\;N \;\;\;\;\;\;-D\] |
\[ FN = 94.3\;\; N \;\;\;\;\;\;-B\] |
Click here to show solutionChoose the correct answer
In the figure below, an object is placed on a rough horizontal plane
A pulling force of 20 Newtons is applied to it at an angle of 30 degrees above the horizontal
The object moves, so the resultant force on the
\[X\] axis equals
\[∑𝐹𝑋=7.3\;\; N \;\;\;\;\;\;-C\] |
\[∑𝐹𝑋=10\;\; N \;\;\;\;\;\;-A\] |
\[ ∑𝐹𝑋=9.6\;\;N \;\;\;\;\;\;-D\] |
\[ ∑𝐹𝑋=2.4\;\; N \;\;\;\;\;\;-B\] |
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In the figure below, an object weighing 26 Newtons is placed on a rough horizontal plane
A pulling force of 20 Newtons is applied to it at an angle of 30 degrees above the horizontal
The object moves. If the kinetic friction force is 10 Newtons, then the coefficient of kinetic friction
equals
\[ 𝜇K = 0.542 \;\;\;\;\;\;-C\] |
\[ 𝜇K = 0.43 \;\;\;\;\;\;-A\] |
\[ 𝜇K = 0.384 \;\;\;\;\;\;-D\] |
\[ 𝜇K = 0.625\;\;\;\;\;\;-B\] |
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Choose the correct answer
Three concurrent forces acted on an object as shown in the figure below
The resultant force
on the horizontal axis and on the vertical axis equals
\[ FX=91.2 N \;\;\;,\;\;\; FY= 40 N \;\;\;\;\;\;-C\] |
\[ FX=-131.2 N\;\;\; ,\;\;\; FY= -10 N \;\;\;\;\;\;-A\] |
\[ FX=-0 N \;\;\;,\;\;\; FY= 0 N\;\;\;\;\;\;-D\] |
\[ FX=11.2 N \;\;\;,\;\;\; FY= -40 N\;\;\;\;\;\;-B\] |
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