Download 04 Forces WS08 [v6.0]

Honors Physics
Concurrent Forces, Resultant Forces, Equilibrant Forces, Components of Force
Worksheet- Forces: Sec. 4.1 to 4.5
1. An object slides on a frictionless plane that makes an angle of 20° with the horizontal. The
object is released from rest at t= 0.
(a) What is the acceleration of the object down the incline? (Answer: 3.4 m /s2 )
(b) How fast is the object moving at t= 4.0 s? (Answer: 13 m/s)
(c) How far does the object move from t= 0 to t= 4.0€s? (Answer: 27 m)
2. The 30 kg block slides down the left incline in the following€frictionless system.
30 kg
€
€
3.
20 kg
€
30 °
45°
2
Find the magnitude of the acceleration of the blocks. (Answer: .17 m /s )
€
20°
€
30 °
€
€ 60 kg
(a) Find the tension in the left string. (Answer: 660 N)
(b) Find the tension in the right string. (Answer: 720 N)
€
4. A pulley is used to support a weight as shown.
String 1
String 2
What angle does String 1 make with the horizontal? (Answer: 45°)
5. A picture whose mass is 5.6 kg is hung on a wall using a wire. The part of the wire to the left
of the fastener has the same length as the part to the right so that the picture hangs with its long
sides horizontal, as shown.
80°
€
5.6 kg
What is the tension in the wire? (Answer: 36 N)
6. A man pushes on a lawn mower handle with a force of 240 N. The handle makes an angle
of 40.0° with the horizontal.
(a) What is the component of the force that tends to push the lawn mower forward?
(Answer: 184 N)
(b) What is the component of the force that tends
€ to press the lawn mower against the ground?
(Answer: 154 N)
7. A block slides down a nearly frictionless incline. The incline makes an angle of 25° with the
horizontal. The block starts from rest.
2
(a) What is the acceleration of the block down the incline? (Answer: 4.1 m /s )
(b) How fast is the object moving 3.0 s after it is released? (Answer: 12 m/s)
(c) How far does the object move during the first 3.0 s after it is released?
(Answer: 18 m or 19 m)
€ 20 m long incline?
(d) How long will it take the object to reach the bottom of the
(Answer: 3.1 s)
€
8. Suppose M1 = 15 kg, M 2 = 9.0 kg and θ = 40°. Ignore the effects of friction. Assume
mass M1 moves down the incline and mass M 2 is lifted.
€
€
€
€
M1
€
M2
€
θ
(a)
(b)
(c)
(d)
(e)
9. (a)
(b)
(c)
(d)
(e)
€
Write an equation
€ that relates g, M1 , θ , T (the tension in the rope joining the masses) and
a (the magnitude of the acceleration of the masses). Take the direction down the incline
(the direction M1 moves) as positive.
(Answer: M1gSin θ − T = M1 a )
€ g, a, T and M . Take upward (the direction M moves) to be
Write an equation that€relates
2
2
the positive direction. (Answer: T − M 2 g = M 2 a )
€ is the acceleration of the masses? (Answer: .26 m /s2 )
What
€
What is the tension in the rope? (Answer: 91 N)
€ how far will M1 move during the
€ first 6.4 s after it is
If the masses start from rest then
€
released? (Answer: 5.3 m or 5.4 m)
€
When two or more forces act at the same point on an object, the forces are said to
be _____ forces. (Answer: concurrent)
€
Two forces act at a point on an object. The force that would have the same effect as the
original two forces is called the _____. You may think of this force as the “sum” of the
two forces. (Answer: resultant)
You find the force of part (b) using a process called _____.
(Answer: composition of force)
Two forces, perpendicular to each other, are found that have the same effect on an object as
a single force F. Each of the two forces is said to be a ____ of force F.
(Answer: component)
You find the forces of part (d) using a process called _____.
(Answer: resolution of force)
10. In the following diagram, vector ____ + vector ____ = vector ____
B
C
A
(Answer: vector C + vector A = vector B or vector A + vector C = vector B)
11. Draw a sketch that indicates how you would construct the resultant R and equilibrant E of
vectors A and B.
A
B
Answer:
A
E
R
B
12. A 65.0 N force acts on a 4.50 kg object in the direction 55.0° north of east. An 85.0 N
concurrent force acts on the object in the direction 35.0° north of west. The forces act on the
object for 7.90 s.
(a) Find the magnitude and direction of the resultant of the two forces acting on the object.
(Answer: 107 N, 72.4° N of W)
(b) Find the magnitude and direction of the object’s acceleration.
(Answer: 23.8 m /s2 , 72.4° N of W)
(c) If the object starts from rest then how far will it travel during the time the forces act?
(Answer: 742 m or 743 m)
13. (a) Can an
€ object moving in a circle be in equilibrium? (Answer: no)
(b) A stone is released from rest. The instant after the stone is released, its speed is zero.
Is the stone in equilibrium the instant after it is released? (Answer: no)
(c) A puck glides on a frictionless air table. Is the puck in equilibrium? (Answer: yes)
(d) An object moves in a straight line. Does the net force on the object always equal zero?
(Answer: no)
(e) An object moves at constant speed. Does the net force on the object always equal zero?
(Answer: no)
(f) An object moves in a straight line at constant speed. Does the net force on the object
always equal zero? (Answer: yes)
14. A 9.0 N force and a 12 N force act concurrently on an object.
(a) What is the smallest possible resultant of the two forces? (Answer: 3.0 N)
(b) What is the largest possible resultant of the two forces? (Answer: 21 N)
15. A 35 kg mass is pulled across a nearly frictionless surface. The mass is pulled to the right
by a 45 N force that makes an angle of 25° with the horizontal. The mass has a velocity
of 5.0 m/s to the right at time t= 0.
(a) What is the acceleration of the mass? (Answer: 1.2 m /s2 )
(b) How far does the mass have to be pulled before its velocity is 12 m/s?
(Answer: 50 m or 51 m)
(c) How far does the mass travel in the first 6.0 s? (Answer: 51 m or 52 m)
€
16. A block rests on an inclined plane. The angle that the incline makes with the horizontal is
slowly
€ increased.
(a) The component of the block’s weight that acts parallel to the incline (increases, decreases,
remains the same). (Answer: increases)
(b) The normal force that the incline exerts on the block (increases, decreases,
remains the same). (Answer: decreases)
17. A sign of mass 30 0 kilograms is fastened to a wall using a chain and a horizontal metal bar.
The chain makes an angle 30 ° with the horizontal.
€
€
30 °
€
30 0 kg
€
Suppose the mass of the sign is m, the chain makes angle θ with the horizontal, T is the tension
in the chain and C is the compression in the bar.
(a) Write an equation relating T, C and θ by considering equilibrium in the horizontal
direction. (Answer: −T Cos θ + C = 0 )
€
(b) Write an equation relating T, m and θ by considering
equilibrium in the vertical direction.
(Answer: T Sin θ − mg = 0)
(c) What is the magnitude of €
the tension in the chain? (Answer: 5900 N)
(d) What is the€magnitude of the compression in the metal bar? (Answer: 5100 N)
€
€
18. Find the magnitude and direction of the equilibrant of the following two concurrent forces.
520 N, 30.0° north of east and
380 N, 40.0° west of north (not north of west)
(Answer: 588 N, 69.5° south of west)
€
€
19. Consider again the pulley system of question 2. The blocks are released from rest.
(a) What is the tension in the rope connecting the masses? (Answer: 140 N)
(b) How fast does the 30 kg block move after it has traveled 4.0 m? (Answer: 1.2 m/s)
HOMEWORK
€
GUIDE
Section in the
Notes
Worksheet Problems
4.2
10. 12, 14
4.3
11. 13, 18
4.4
9
4.5
1, 2, 3, 4, 5, 6, 7, 8, 15, 16, 17, 19