Vector and Scalar
1. Among the following options, which are scalar-vector pairs…
A. Force – acceleration
B. Pressure – force
C. Displacement – speed
D. Electric current – pressure
Solution :
Force = vector, acceleration = vector
Pressure = scalar, force = vector
Displacement = vector, speed = scalar
Electric current = scalar, pressure = scalar
The correct answer is B.
2.
The correct answer is shown by number…
A. 1 and 4
B. 1 and 2
C. 2 and 3
D. 3 and 4
Solution :
Speed = scalar
Displacement = vector
Weight = vector
Acceleration = vector
The correct answer is C.
[irp]
Components of vectors
3. Two vectors, F1 = 20 N and F2 = 30 N, have direction as shown in the figure below. Determine the resultant of components of vectors in x-axis and y-axis.
A. 5√3 N and -25 N
B. -5√3 N and 25 N
C. 25 N and 5√3 N
D. 30 N and 25√3 N
Known :
F1 = 20 Newton
Angle between F1 and x axis = 30o
F2 = 30 Newton
Angle between F2 and x axis =30o
Wanted : Fx and Fy
Solution :
F1x = F1 cos 30o = (20)(0.5√3) = 10√3 Newton (plus sign because points to +x axis)
F1y = F1 sin 30o = (20)(0.5) = 10 Newton (plus sign because point to +y axis)
F2x = F2 cos 30o = (30)(0.5√3) = -15√3 Newton (minus sign because points to -x axis)
F2y = F2 sin 30o = (30)(0.5) = 15 Newton (plus sign because points to +y axis)
The resultant of the x component :
Fx = F1x + F2x = 10√3 N – 15√3 N = -5√3 Newton
The resultant of the y component :
Fy = F1y + F2y = 10 N + 15 N = 25 Newton
The correct answer is B.
[irp]
The resultant of two vectors
4. Two children A and B push a block, if A push the block southward with force of 400 N and at the same time B push the block eastward with force of 300 N, then determine the resultant of force A and B.
A. 100 N southward
B. 100 N eastward
C. 500 N southeastward
D. 700 N southeastward
Known :
U = north, T = east, S = south, B = west
TL = northeast, TG = southeast, BD = southwest, BL = northwest
A = 400 Newton southward
B = 300 Newton eastward
Wanted: magnitude and direction of net force (R)
Solution :
The correct answer is C.
[irp]
The resultant of the vector of displacement
5. Someone riding a motorcycle from home 6 km to north then 8 km to east. Determine the final position of the person from the initial position.
A. 14 km northeast
B. 14 km southwest
C. 10 km northeast
D. 10 km northwest
Known :
Wanted: magnitude and direction of the resultant of displacement
Solution :
The correct answer is C.
6.
Based on the figure above, If 1 square represents 1 km, then what is the total displacement.
Solution :
Distance = A + B + C = 6 + 6 + 2 = 14 km
Displacement = R = 12 km
[irp]
7. A car travels from A to B along 30 km north, then 60 km east, then 110 km south. Determine the displacement of the car from A to D.
Solution :
AA’ = 60 km
A’D = 110 km – 30 km = 80 km
[irp]
8. A car travels from town A to town B 100 km north, then to town C 60 km east, and then to town D 20 km south. Determine the displacement of the car.
Solution :
D’D = 60 km
AD’ = 100 km – 20 km = 80 km