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Review Test #4: Vectors & Two-Dimensional Forces
Reading: Ch. 5, p.p. 118 - 139
Topics: Vector Addition, Equilibrium, Inclines
Labs & Activities: Treasure Hunt
Equations:
Fg= mg
a = Fnet
m
soh
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Ff = μFN
cah
c² = a² + b²
toa
Know a vector has magnitude and direction.
Be able to draw vectors tip-to-tail.
Know the resultant is the vector that points from the start to the finish when 2 or
more vectors are drawn tip-to-tail.
Be able to find the resultant graphically and algebraically.
Be able to identify and diagram the forces on an object.
Be able to break forces at angles into components.
Know an object is in equilibrium when the forces acting on the object are balanced.
Know an object in equilibrium will move at a constant speed or not at all.
Be able to identify forces that are balanced.
With inclines, be able to break the force of gravity into components.
Know the relationship between the angle of an incline and the components of gravity.
Practice Questions & Problems
1. a. List four ways to describe the direction of the vector.
b. Calculate the components of the vector shown.
20⁰
15 N
2. A girl jogs 2.5 miles west and 5 miles north. Calculate her resultant displacement.
3. Two displacement vectors each with a y-component of 10 km are added together to
form a resultant which makes an angle of 60º with the horizontal. What is the
magnitude of the resultant?
4. A hiker walks 25.5 km at 35º south of east. On the next day he walks 41 km at 65º
north of east. What is his total displacement?
5. A man pulls a 0.85 kg book across a table with a force of 7 N at an angle of 24º to the
horizontal. The coefficient of friction for the book on the table is 0.25. Calculate
the book’s acceleration.
6. A 9800N railroad car is being pulled on tracks of negligible friction by ropes tied to
two horses as shown in the top view below. The net force on the car is 500 N to the
right. a) Calculate the tension in each rope. b) Calculate the car’s acceleration.
80⁰
7. Calculate the tension in the cables shown.
T
T
10⁰
10⁰
20 kg
8. A 14 kg box is pushed along the floor with a force of 68 N that acts at an angle of 35º
below the horizontal. The block accelerates to the right at 1.45 m/s². Find the
coefficient of friction between the block and the floor.
9. An 80 kg sled is pulled up a hill that has an incline of 27 °. If the coefficient of
friction between the sled and the snow is 0.12, how hard must a child pull the sled to
accelerate it at 0.75 m/s² ?
10. A 5 kg block is held in equilibrium on a frictionless incline of 30° by a force, F, as
shown. Find the magnitude of F and the normal force.
F