1 Which of the following is the correct unit of k in
the equation of a damped harmonic oscillator
given as
, where b is the damping factor and all the
symbols have their usual meaning?
2 If s is distance and t is time, what must be the
dimensions of a and b in the equation
?
,
,
,
,
3 What are the dimensions of pressure gradient?
4 Which of the following quantities have the same
dimensions?
moment and power
work and power
torque and work
work and upthrust
5 Which of the following equations is not
dimensionally consistent? the symbols have their
usual meaning.
6 Given three vectors
,
,
, calculate
6
9
7 A man walks
due east and then
. Find his resultant displacement.
13.7 m,
14.6 m,
10.0 m,
14.6m,
8 A man leaves the garrage in his house and
drives to a neighbouring town which is twenty
kilometres away from his house on sight-seeing.
He returns home to his garrage two hours after.
What is his average velocity from home in km/h?
10
0
20
40
9 Which of the following quantities is an example
of a vector or cross product?
momentum
work
density
torque
10 Which of the following is NOT correct?
11 Which of the follwing statements is correcct?
An object can have a constant velocity even
though its speed is changing
An object can have a constant speed even
though its velocty is changing
An object can have zero acceleration and
eventually reverses its direction
An object can have constant velocity even
though its acceleration is not zero
12 Which of the following correctly gives the
direction of a vector product
?
If the right thumb points in the direction of
and the other fingers point in the direction of
, then the palm pushes in the opposite direction
of
If the right is held such that the curled
fingers follow the rotation of
into
, then the extended right thumb points in the
direction of
If the left thumb points in the direction of
and the other fingers point in the direction of
, then the palm pushes in the direction of
The direction of retreat of the right-handed
screw when turned from
to
through the smaller angle.
13 Two vectors
and
have components, in arbitrary units,
,
,
,
. Find the angle between
and
14 When we describe the motion of an object we
are dealing with the part of mechanics called
statics
translation
dynamics
kinematics
15 Which of the following physical concepts best
explains why passengers in fast moving cars
should always fasten their seat-belts?
inertia
terminal velocity
moment of inertia
acceleration
16 An observer can describe the motion of an
object as "translational" if
the axes of the reference frame imagined to
be attached to the object
,
and
always remain parallel to the axes of his own
reference frame
,
and
the object moves in a curved path in such a
way that
,
and
may rotate about their origin
the motion of the object may not be
represented by the motion of its centre of mass
all the constituent particles of the object
undergo different displacements at the same time
17 An object is thrown upward from the edge of a
building with a velocity of 20 m/s. Where will the
object be 3s after it was thrown?
16m
22m
18 The displacement of a particle along the X-
axis is given as
, where x is in metres and t in seconds. Calculate
its average velocity in the time interval between 2
s and 3 s.
21 m/s
40 m/s
46 m/s
25 m/s
19 A bullet is straight upward with a velocity of
100 m/s from the top of a building 100 m high.
Find its maximum height above the ground
500 m
600 m
1000 m
300 m
20 The displacement of a particle along the X-
axis is given as
, where x is in metres and t in seconds. Calculate
its instantaneous velocity 2 s.
46 m/s
40 m/s
20 m/s
25 m/s
1 Which of the following is the correct unit of k in
the equation of a damped harmonic oscillator
given as
, where b is the damping factor and all the
symbols have their usual meaning?
==============================
F = - k x
Newtons = -k * meters
k is therefore in Newtons/meter
Now you do some.
Note, many of your questions are incomplete. For example number 2 does not give the equation that a and b are used in. Is this some kind of a joke or are you not reading what you write?
=================================
2 If s is distance and t is time, what must be the
dimensions of a and b in the equation
?
,
,
,
,
3 What are the dimensions of pressure gradient?
4 Which of the following quantities have the same
dimensions?
moment and power
work and power
torque and work
work and upthrust
5 Which of the following equations is not
dimensionally consistent? the symbols have their
usual meaning.
6 Given three vectors
,
,
, calculate
6
9
7 A man walks
due east and then
. Find his resultant displacement.
13.7 m,
14.6 m,
10.0 m,
14.6m,
8 A man leaves the garrage in his house and
drives to a neighbouring town which is twenty
kilometres away from his house on sight-seeing.
He returns home to his garrage two hours after.
What is his average velocity from home in km/h?
10
0
20
40
9 Which of the following quantities is an example
of a vector or cross product?
momentum
work
density
torque
10 Which of the following is NOT correct?
11 Which of the follwing statements is correcct?
An object can have a constant velocity even
though its speed is changing
An object can have a constant speed even
though its velocty is changing
An object can have zero acceleration and
eventually reverses its direction
An object can have constant velocity even
though its acceleration is not zero
12 Which of the following correctly gives the
direction of a vector product
?
If the right thumb points in the direction of
and the other fingers point in the direction of
, then the palm pushes in the opposite direction
of
If the right is held such that the curled
fingers follow the rotation of
into
, then the extended right thumb points in the
direction of
If the left thumb points in the direction of
and the other fingers point in the direction of
, then the palm pushes in the direction of
The direction of retreat of the right-handed
screw when turned from
to
through the smaller angle.
13 Two vectors
and
have components, in arbitrary units,
,
,
,
. Find the angle between
and
14 When we describe the motion of an object we
are dealing with the part of mechanics called
statics
translation
dynamics
kinematics
15 Which of the following physical concepts best
explains why passengers in fast moving cars
should always fasten their seat-belts?
inertia
terminal velocity
moment of inertia
acceleration
16 An observer can describe the motion of an
object as "translational" if
the axes of the reference frame imagined to
be attached to the object
,
and
always remain parallel to the axes of his own
reference frame
,
and
the object moves in a curved path in such a
way that
,
and
may rotate about their origin
the motion of the object may not be
represented by the motion of its centre of mass
all the constituent particles of the object
undergo different displacements at the same time
17 An object is thrown upward from the edge of a
building with a velocity of 20 m/s. Where will the
object be 3s after it was thrown?
16m
22m
18 The displacement of a particle along the X-
axis is given as
, where x is in metres and t in seconds. Calculate
its average velocity in the time interval between 2
s and 3 s.
21 m/s
40 m/s
46 m/s
25 m/s
19 A bullet is straight upward with a velocity of
100 m/s from the top of a building 100 m high.
Find its maximum height above the ground
500 m
600 m
1000 m
300 m
20 The displacement of a particle along the X-
axis is given as
, where x is in metres and t in seconds. Calculate
its instantaneous velocity 2 s.
46 m/s
40 m/s
20 m/s
25 m/s
1. The correct unit of k in the equation of a damped harmonic oscillator is kg/s^2. To obtain this unit, we need to consider the dimensions of each term in the equation. The displacement x has dimensions of meters (m), the second derivative of x with respect to time squared (d^2x/dt^2) has dimensions of m/s^2, and the damping factor b has dimensions of kg/s. Therefore, the dimension of k, which is the ratio of the damping force to the displacement, is kg/s^2.
2. In the equation s = at^2 + bt + c, where s is distance and t is time, the dimensions of a and b must be determined. The dimensions of distance are meters (m) and the dimensions of time are seconds (s). To determine the dimensions of a and b, we can equate the dimensions on both sides of the equation. The dimensions of at^2 are m/s^2, the dimensions of bt are m/s, and the dimensions of c are m. Therefore, to balance the dimensions on both sides of the equation, a must have dimensions of m/s^2 and b must have dimensions of m/s.
3. The dimensions of pressure gradient are (force/area)/length or N/m^3. To calculate the dimensions, we consider that pressure is force/area and length is just meters. Therefore, the dimensions of pressure gradient are N/m^3.
4. The quantities that have the same dimensions are moment and torque. Both moment and torque have dimensions of force times distance, which is N⋅m. Work and power have different dimensions, with work having dimensions of force times distance and power having dimensions of work done per unit time. Work and upthrust also have different dimensions, with work having dimensions of force times distance and upthrust having dimensions of force. Therefore, moment and torque are the quantities that have the same dimensions.
5. To determine which equation is not dimensionally consistent, we need to consider the dimensions of each term within the equation and see if they match. Unfortunately, the equations mentioned in question 5 are not provided, so we cannot determine which equation is not dimensionally consistent.
6. To calculate the resultant of three vectors a, b, and c, we need to add them together. The resultant vector R is given by R = a + b + c. Add the corresponding components of each vector to get the resulting x and y components of R.
7. To find the resultant displacement of a man who walks due east and then due north, we can visualize this as two vectors added together. The Eastward displacement of 10.0 m is along the x-axis, and the northward displacement of 14.6 m is along the y-axis. We can use the Pythagorean theorem to calculate the magnitude of the resultant displacement: magnitude = sqrt((10.0)^2 + (14.6)^2) = 18.0 m. To find the direction of the resultant displacement, we can use trigonometry. The angle θ can be found using the tangent function: θ = arctan(14.6/10.0) = 56.3 degrees. Therefore, the resultant displacement is 18.0 m at an angle of 56.3 degrees with respect to the positive x-axis.
8. To calculate the average velocity, we need to divide the total distance traveled by the total time taken. In this case, the man drives 20 kilometers away from his house and then returns home. The total distance traveled is 40 kilometers (20 km out + 20 km back). The total time taken is 2 hours. To find the average velocity, divide the total distance by the total time: average velocity = 40 km / 2 h = 20 km/h.
9. An example of a vector or cross product is torque. Torque is calculated as the vector product of the force applied to an object and the lever arm through which the force acts. The magnitude of torque is given by the product of the magnitude of the force and the perpendicular distance from the axis of rotation to the line of action of the force. Thus, torque is an example of a vector or cross product.
10. The statement "An object can have constant velocity even though its speed is changing" is not correct. Velocity is a vector quantity that includes both the magnitude (speed) and the direction of motion. If an object's speed is changing, then by definition its velocity is also changing. Therefore, this statement is not correct.
11. The correct statement is "An object can have a constant velocity even though its acceleration is not zero." Velocity measures the rate of change of position, while acceleration is the rate of change of velocity. An object can have a constant velocity if its speed and direction remain constant, even if it is accelerating (changing its velocity). As long as the direction of acceleration is perpendicular or tangential to the direction of motion, the object's velocity can remain constant.
12. The correct statement is "If the right thumb points in the direction of v and the other fingers point in the direction of u, then the palm pushes in the direction of w." The right-hand rule is used to determine the direction of the vector product (also called the cross product) of two vectors. The right thumb points in the direction of the first vector, while the other fingers point in the direction of the second vector. The extended right-hand palm represents the direction of the cross product.