Gravity
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Gravity as PDF for free.
More details
- Words: 2,313
- Pages: 14
(b)
LESSON 2.8 . Analysing forces in Forces in Equilibrium The principle of the forces in equilibrium states, “ When forces act upon an object , the object is said to be in a state of equilibrium when the resulting force acting on the object is zero ( no net force acting upon it) ” When the equilibrium is reached, then the object is in two states, that is (i) remains stationary (if the object is stationary) (ii) moves at a constant velocity ( if the object is moving) Based on , F = ma atau a = F
Weight = Tension (c)
Buoyant force = Weight
m When the equilibrium of forces is achieved, then, F = 0 , hence a =0 Thus a = 0 , it means the object remains stationary or moves at a constant velocity.
(d)
Newton’s Third Law of Motion Newton’s third law of motion states , “ To every action there is an equal but opposite direction”
Weight = Normal reaction (e)
Examples Forces in Equilibrium (a)
Weight = Normal reaction
Weight = Normal reaction
49
Pulling force = Frictional force
Two Forces in Equilibrium
(f)
P + Q=0 P =-Q Example 1 Figure shows a stationary wooden block of mass 2 kg resting on a table.
Weight = Lifting force Driving force = Dragging force (g)
Calculate (a) the weight of the wooden block (b) the normal reaction Solution
Three Forces in Equilibrium Weight = Normal reaction Engine thrust = Air resistance + Frictional force (h) P + Q +R=0 When three forces in equilibrium the triangle of forces in one direction (in order) Example 2 The following figure shows a steel sphere of mass 12 kg suspended from a length of rope which is pulled to the side by a horizontal force of M. The tension of another rope is N.
Buoyant force = Weight of load + Weight of helium gas
50
In this method the tail of the first vector is joined to the tail of second vector and then draw a parallelogram. The diagonal represents the resultant force. Triangle method: In this method the tip of the first vector is joined to the tail of second vector and then draw a line to complete the triangle. The third side represents the resultant force.
(a) Draw a triangle of forces. (b) Calculate the value of (i) M (ii) N
Terdapat dua kaedah menentukan
Solution
daya paduan yang bagi daya-daya tidak selari. Example 3
Resultant force
Find the resultant force for the following figure:-
Force is a vector quantity and hence it has magnitude and direction. Two or more forces which act on an object can be combined into a single force called the resultant force. If two forces are in same line, vector addition is easy. We simply add the forces if both pull or push together; subtract them if one is in the opposite direction. If they are at an angle, the resultant force can be determined by the triangle method and the parallelogram method. Parallelogram method :
Solution:
51
Example 4 The figure shows a trolley is pulled by two forces
Fx = F cos θ Fy = F sin θ
What is the magnitude and the direction of the resultant force acting on the trolley.
• •
Solution
θ is an angle between the force F to the horizontal line the sign of the force depend on the quadrant where the force , F is placed
For an object on a inclined plane, the weight,W of the object can be resolved into two components ; (i) parallel to inclined plane, A (ii) perpendicular to inclined plane,B Example 5 Figure shows a boat is pulled by two forces. Calculate the magnitude of the resultant force acting on the trolley. Solution:
Resolution of forces A = W sin θ B = W kos θ
A force can be resolved into two components, that is, (i) the horizontal component, Fx and (ii) the vertical component , Fy
52
Example 6 Find the values of Px and Py for the following figures.
TUTORIAL 2.8 1 When the equilibrium is reached an object A B C a
remains stationary moves at a constant velocity remains stationary or moves at constant velocity
2 Solution:
Example 7 Figure shows a stationary wooden block of mass 50 g which is placed on a inclined plane that is at an angle of 40o to the horizontal. What is the magnitude of the weight parallel to the inclined plane. Solution
53
Which of the following shows the three forces 5N, 12N and 13 N in equilibrium.
3
Figure shows three forces F1 , F2 and F3 acting at a point.
What is the tension , L? A C E 6
40 N 20 N 5N
B D
30 N 10 N
Figure shows a monkey hangs from the middle of a massless rope.
Which of the following vector diagram represents the forces correctly?
4
If the tension of each strings is 150 N, what is the mass of the monkey?
Figure shows the forces 10 N, P and Q acting at a point in equilibrium.
A C E 7
5 kg 15 kg 30 kg
D
B 10 kg 20 kg
Figure shows three loads suspended from inelastic strings through two smooth pulleys.
What is the magnitude of the force, P ? A C E 5
5.0 N 8.7 N 12.7 N
B D
6.4 N 10.0 N
Figure shows the three forces L , M and N acting on a point O and which are in equilibrium
If the three loads in equilibrium, what is the value of W ? A C E 8
54
8N 16 N 32 N
B
12 N D 24 N
Figure shows a lantern of mass 0.2 kg is suspended by a string that is joined two other strings.
11 Figure shows two forces 9 N and 12 N act at a point O. What is the tension in each string P and Q ? A C E 9
0.86 N 1.74 N 3.48 N
B D
1.00 N 2.00 N Which of the following figures show the resultant of two forces.
The figure shows three identical pictures are hang differently on a wall .
Which comparison is true about the tension of each strings in the arrangement of P ,Q and R? A Tension in Tension in R B Tension in Tension in R C Tension in Tension in Q D Tension in Tension in P 10
12 Figure shows two forces 3 N and 4 N which are perpendicular each other.
P > Tension in Q > Q > Tension in P > P > Tension in R > R > Tension in Q >
Which of the following produces the largest resultant force?
What is the angle between the resultant force to the force of 4 N? A C E
55
53.1o 42.0o 23.5o
B D
48.8o 36.9o
13 Figure shows two forces 5 N and 4 N act at a point and make an angle of 60o with each other.
What is the magnitude of the resultant force acting on the ground? What is the resultant force ? A C E
12.5 N 7. 8 N 1.5 N
B D
A C E
9.2 N 3.0 N
217 N 560 N 1732 N
D
B 433 N 866 N
16 Figure shows two forces 15 N and 10 N are applied at a point O.
14 Figure shows two forces F N respectively act at a point O and make an angle of 120o with each other.
What is the resultant force? A C E What is the resultant force? A ¼FN B ½FN C FN D ¾FN E 2F N
9.5 N 10.6 N 12.4 N
B D
10.2 N 11.8 N
17
15 Figure shows two lengths of cables, PQ and RQ are used to hold a flagpole upright. Each cable has a tension 1 000 N and makes and angle 60o to the surface of the ground.
Based on the figure above , which of the following figures show the resultant of two forces
56
What is the vertical component of the force?
18 Which of the following figures
give the largest resultant force of three forces.
A C E
27.5 N 9.5 N 4.5 N
B
12. 5 N D 7.5 N
21 Figure shows a gardener pushes a lawnmower with a force 500 N at an angle 60o to the surface of the field.
19 Figure shows four forces 3 N, 8 N, 8 N and 20 N acting at a point. What is the force pushing the lawnmower forward ? . A C E
50 N 250 1000 N
B D
125 N 500 N
What is the resultant force acting at the point? A C E
5N 8N 13 N
B D
6N 10 N 22 Figure shows a small carton of weight 50 N is placed on a inclined plane makes an angle 30o to the horizontal .
20 Figure shows a trolley being pushed by a 15 N force on a floor.
57
5.14 ms-2 B 6.13 ms C 6.42 ms-2 D 7.66 ms-2 E 8.00 ms-2 A
-2
25 Figure(a) shows a situation in tug of war contest. The rope remains stationary at central line although the rope is pulled at opposite ends by both of teams. F1 and F2 are the forces acting at the rope.
What is the value of F ? A C E
50 N 20 N 5N
B D
25 N 10 N
23 Figure shows a trolley of mass 2 kg being pulled by a 10 N force on a rough surface . The frictional force between the rough surface and the trolley is 2 N.
Figure (a) Figure (b) shows a car is moving at an uniform velocity 20 ms-1 along a straight road. F3 dan F4 are the forces acting at the car.
What is the acceleration of the trolley? A
0.5 ms-2
B
C ms-2 E
1.5 ms-2
D
2
(a)
1.0 ms-
Figure (b) Name the force (i) F1
3.0
……………………………… …… (ii)
6.0 ms-2
24 Figure shows a toy car of mass 0.8 kg which is released from rest and is now moving down a smooth inclined plane. The inclined plane makes an angle of 50o with the horizontal plane.
F4
……………………………… ……. (b) What is the magnitude of resultant force between (i) F1 and F2 ……………………………… …… (ii)
F3 and F4
……………………………… ….. (c) Based on your answers in (b)(i) and (b)(ii) also the informations in Figure(a) and Figure(b), relate the situations
What is acceleration experienced by the toy car
58
to deduce a relevant physics concept and hence name the concept.
……………………………………… ……………… (c) What will happen when the forward thrust is increased?
……………………………………… …………
…………………………………………… ………… (d) Why the cyclist thrown forward when the bicycle runs over a stone.?
……………………………….…… …………... (d) (i) What will happen to the motion of the car if F3 is 8 000N ?
…………………………………………… ………… (e) Explain why the cyclist can gets serious injuries if he falls into the road which the surface is very hard.
………………………………… ……….. (ii) Give one reason for your answer in (d)(i).
……………………………………… ………………
………………………………… ………..
…………………………………………… …………
26 Figure shows a cyclist is riding along a road at a constant velocity. The total of downward force acting on the bicycle and the cyclist is 650 N. The normal reaction of the front tyre is 300 N and forward thrust is 200 N.
…………………………………………… …………
27 Figure shows a ball of mass 4kg
suspended from a length of rope NO which is pulled by two ropes NP and NM.
(a) Calculate the normal reaction ,P acting on the rear tyre .
(b) Give one reason why the total resistance,Q should be 200 N at that moment?
59
(a)
Draw a vector diagram to show the action of the forces.
(b) Determine (i) the value of T
(ii) the value of angle k
(a) Determine the resultant force along x-axis
(c) If the rope NO is cut , the time taken for the ball to reach the floor is 2.5 s . (i) What is the velocity of the ball when it reaches the floor?
(b) Determine the resultant force along y-axis
(ii) What is the height of the ball from the floor.
(c) Determine the resultant force acting on the ship.
28 Figure shows a ship is pulled horizontally by two boats with two forces 6 kN and 10 kN.
29 Figure shows a man pulls a trolley full of groceries with a force 70 N at an angle 20o to the surface of the floor.
60
(a) What is (i) the horizontal component of the pulling force?
(ii) the vertical component of the pulling force?
30 Figure show a sampan in river is pulled by a workman. The workman pulls with a force of 400 N and the rope used make an angle 50o with the bank of the river.
(b) If the total mass of the trolley and the groceries is 60 kg, determine (i) the acceleration of the trolley
(ii) the force cause by the trolley and the groceries only acting on floor.
(a) What is the force pulling the sampan forward. (b) What is the force pulling the
sampan to the bank?
(iii) the total force acting on the floor.
(c) (i) If the length of the rope is increased , how easier for the workman to pull the sampan forward?
(d) If the trolley is pushed by the man at a same angle as the trolley is pulled , what is the total force acting on the floor.
........................................... ................. (ii) Give the reason for your answer in (c)(i) ………………………………… ……….. ………………………………… ……….. ………………………………… ………..
61
………………………………… ………..
62
LESSON 2.8 . Analysing forces in Forces in Equilibrium The principle of the forces in equilibrium states, “ When forces act upon an object , the object is said to be in a state of equilibrium when the resulting force acting on the object is zero ( no net force acting upon it) ” When the equilibrium is reached, then the object is in two states, that is (i) remains stationary (if the object is stationary) (ii) moves at a constant velocity ( if the object is moving) Based on , F = ma atau a = F
Weight = Tension (c)
Buoyant force = Weight
m When the equilibrium of forces is achieved, then, F = 0 , hence a =0 Thus a = 0 , it means the object remains stationary or moves at a constant velocity.
(d)
Newton’s Third Law of Motion Newton’s third law of motion states , “ To every action there is an equal but opposite direction”
Weight = Normal reaction (e)
Examples Forces in Equilibrium (a)
Weight = Normal reaction
Weight = Normal reaction
49
Pulling force = Frictional force
Two Forces in Equilibrium
(f)
P + Q=0 P =-Q Example 1 Figure shows a stationary wooden block of mass 2 kg resting on a table.
Weight = Lifting force Driving force = Dragging force (g)
Calculate (a) the weight of the wooden block (b) the normal reaction Solution
Three Forces in Equilibrium Weight = Normal reaction Engine thrust = Air resistance + Frictional force (h) P + Q +R=0 When three forces in equilibrium the triangle of forces in one direction (in order) Example 2 The following figure shows a steel sphere of mass 12 kg suspended from a length of rope which is pulled to the side by a horizontal force of M. The tension of another rope is N.
Buoyant force = Weight of load + Weight of helium gas
50
In this method the tail of the first vector is joined to the tail of second vector and then draw a parallelogram. The diagonal represents the resultant force. Triangle method: In this method the tip of the first vector is joined to the tail of second vector and then draw a line to complete the triangle. The third side represents the resultant force.
(a) Draw a triangle of forces. (b) Calculate the value of (i) M (ii) N
Terdapat dua kaedah menentukan
Solution
daya paduan yang bagi daya-daya tidak selari. Example 3
Resultant force
Find the resultant force for the following figure:-
Force is a vector quantity and hence it has magnitude and direction. Two or more forces which act on an object can be combined into a single force called the resultant force. If two forces are in same line, vector addition is easy. We simply add the forces if both pull or push together; subtract them if one is in the opposite direction. If they are at an angle, the resultant force can be determined by the triangle method and the parallelogram method. Parallelogram method :
Solution:
51
Example 4 The figure shows a trolley is pulled by two forces
Fx = F cos θ Fy = F sin θ
What is the magnitude and the direction of the resultant force acting on the trolley.
• •
Solution
θ is an angle between the force F to the horizontal line the sign of the force depend on the quadrant where the force , F is placed
For an object on a inclined plane, the weight,W of the object can be resolved into two components ; (i) parallel to inclined plane, A (ii) perpendicular to inclined plane,B Example 5 Figure shows a boat is pulled by two forces. Calculate the magnitude of the resultant force acting on the trolley. Solution:
Resolution of forces A = W sin θ B = W kos θ
A force can be resolved into two components, that is, (i) the horizontal component, Fx and (ii) the vertical component , Fy
52
Example 6 Find the values of Px and Py for the following figures.
TUTORIAL 2.8 1 When the equilibrium is reached an object A B C a
remains stationary moves at a constant velocity remains stationary or moves at constant velocity
2 Solution:
Example 7 Figure shows a stationary wooden block of mass 50 g which is placed on a inclined plane that is at an angle of 40o to the horizontal. What is the magnitude of the weight parallel to the inclined plane. Solution
53
Which of the following shows the three forces 5N, 12N and 13 N in equilibrium.
3
Figure shows three forces F1 , F2 and F3 acting at a point.
What is the tension , L? A C E 6
40 N 20 N 5N
B D
30 N 10 N
Figure shows a monkey hangs from the middle of a massless rope.
Which of the following vector diagram represents the forces correctly?
4
If the tension of each strings is 150 N, what is the mass of the monkey?
Figure shows the forces 10 N, P and Q acting at a point in equilibrium.
A C E 7
5 kg 15 kg 30 kg
D
B 10 kg 20 kg
Figure shows three loads suspended from inelastic strings through two smooth pulleys.
What is the magnitude of the force, P ? A C E 5
5.0 N 8.7 N 12.7 N
B D
6.4 N 10.0 N
Figure shows the three forces L , M and N acting on a point O and which are in equilibrium
If the three loads in equilibrium, what is the value of W ? A C E 8
54
8N 16 N 32 N
B
12 N D 24 N
Figure shows a lantern of mass 0.2 kg is suspended by a string that is joined two other strings.
11 Figure shows two forces 9 N and 12 N act at a point O. What is the tension in each string P and Q ? A C E 9
0.86 N 1.74 N 3.48 N
B D
1.00 N 2.00 N Which of the following figures show the resultant of two forces.
The figure shows three identical pictures are hang differently on a wall .
Which comparison is true about the tension of each strings in the arrangement of P ,Q and R? A Tension in Tension in R B Tension in Tension in R C Tension in Tension in Q D Tension in Tension in P 10
12 Figure shows two forces 3 N and 4 N which are perpendicular each other.
P > Tension in Q > Q > Tension in P > P > Tension in R > R > Tension in Q >
Which of the following produces the largest resultant force?
What is the angle between the resultant force to the force of 4 N? A C E
55
53.1o 42.0o 23.5o
B D
48.8o 36.9o
13 Figure shows two forces 5 N and 4 N act at a point and make an angle of 60o with each other.
What is the magnitude of the resultant force acting on the ground? What is the resultant force ? A C E
12.5 N 7. 8 N 1.5 N
B D
A C E
9.2 N 3.0 N
217 N 560 N 1732 N
D
B 433 N 866 N
16 Figure shows two forces 15 N and 10 N are applied at a point O.
14 Figure shows two forces F N respectively act at a point O and make an angle of 120o with each other.
What is the resultant force? A C E What is the resultant force? A ¼FN B ½FN C FN D ¾FN E 2F N
9.5 N 10.6 N 12.4 N
B D
10.2 N 11.8 N
17
15 Figure shows two lengths of cables, PQ and RQ are used to hold a flagpole upright. Each cable has a tension 1 000 N and makes and angle 60o to the surface of the ground.
Based on the figure above , which of the following figures show the resultant of two forces
56
What is the vertical component of the force?
18 Which of the following figures
give the largest resultant force of three forces.
A C E
27.5 N 9.5 N 4.5 N
B
12. 5 N D 7.5 N
21 Figure shows a gardener pushes a lawnmower with a force 500 N at an angle 60o to the surface of the field.
19 Figure shows four forces 3 N, 8 N, 8 N and 20 N acting at a point. What is the force pushing the lawnmower forward ? . A C E
50 N 250 1000 N
B D
125 N 500 N
What is the resultant force acting at the point? A C E
5N 8N 13 N
B D
6N 10 N 22 Figure shows a small carton of weight 50 N is placed on a inclined plane makes an angle 30o to the horizontal .
20 Figure shows a trolley being pushed by a 15 N force on a floor.
57
5.14 ms-2 B 6.13 ms C 6.42 ms-2 D 7.66 ms-2 E 8.00 ms-2 A
-2
25 Figure(a) shows a situation in tug of war contest. The rope remains stationary at central line although the rope is pulled at opposite ends by both of teams. F1 and F2 are the forces acting at the rope.
What is the value of F ? A C E
50 N 20 N 5N
B D
25 N 10 N
23 Figure shows a trolley of mass 2 kg being pulled by a 10 N force on a rough surface . The frictional force between the rough surface and the trolley is 2 N.
Figure (a) Figure (b) shows a car is moving at an uniform velocity 20 ms-1 along a straight road. F3 dan F4 are the forces acting at the car.
What is the acceleration of the trolley? A
0.5 ms-2
B
C ms-2 E
1.5 ms-2
D
2
(a)
1.0 ms-
Figure (b) Name the force (i) F1
3.0
……………………………… …… (ii)
6.0 ms-2
24 Figure shows a toy car of mass 0.8 kg which is released from rest and is now moving down a smooth inclined plane. The inclined plane makes an angle of 50o with the horizontal plane.
F4
……………………………… ……. (b) What is the magnitude of resultant force between (i) F1 and F2 ……………………………… …… (ii)
F3 and F4
……………………………… ….. (c) Based on your answers in (b)(i) and (b)(ii) also the informations in Figure(a) and Figure(b), relate the situations
What is acceleration experienced by the toy car
58
to deduce a relevant physics concept and hence name the concept.
……………………………………… ……………… (c) What will happen when the forward thrust is increased?
……………………………………… …………
…………………………………………… ………… (d) Why the cyclist thrown forward when the bicycle runs over a stone.?
……………………………….…… …………... (d) (i) What will happen to the motion of the car if F3 is 8 000N ?
…………………………………………… ………… (e) Explain why the cyclist can gets serious injuries if he falls into the road which the surface is very hard.
………………………………… ……….. (ii) Give one reason for your answer in (d)(i).
……………………………………… ………………
………………………………… ………..
…………………………………………… …………
26 Figure shows a cyclist is riding along a road at a constant velocity. The total of downward force acting on the bicycle and the cyclist is 650 N. The normal reaction of the front tyre is 300 N and forward thrust is 200 N.
…………………………………………… …………
27 Figure shows a ball of mass 4kg
suspended from a length of rope NO which is pulled by two ropes NP and NM.
(a) Calculate the normal reaction ,P acting on the rear tyre .
(b) Give one reason why the total resistance,Q should be 200 N at that moment?
59
(a)
Draw a vector diagram to show the action of the forces.
(b) Determine (i) the value of T
(ii) the value of angle k
(a) Determine the resultant force along x-axis
(c) If the rope NO is cut , the time taken for the ball to reach the floor is 2.5 s . (i) What is the velocity of the ball when it reaches the floor?
(b) Determine the resultant force along y-axis
(ii) What is the height of the ball from the floor.
(c) Determine the resultant force acting on the ship.
28 Figure shows a ship is pulled horizontally by two boats with two forces 6 kN and 10 kN.
29 Figure shows a man pulls a trolley full of groceries with a force 70 N at an angle 20o to the surface of the floor.
60
(a) What is (i) the horizontal component of the pulling force?
(ii) the vertical component of the pulling force?
30 Figure show a sampan in river is pulled by a workman. The workman pulls with a force of 400 N and the rope used make an angle 50o with the bank of the river.
(b) If the total mass of the trolley and the groceries is 60 kg, determine (i) the acceleration of the trolley
(ii) the force cause by the trolley and the groceries only acting on floor.
(a) What is the force pulling the sampan forward. (b) What is the force pulling the
sampan to the bank?
(iii) the total force acting on the floor.
(c) (i) If the length of the rope is increased , how easier for the workman to pull the sampan forward?
(d) If the trolley is pushed by the man at a same angle as the trolley is pulled , what is the total force acting on the floor.
........................................... ................. (ii) Give the reason for your answer in (c)(i) ………………………………… ……….. ………………………………… ……….. ………………………………… ………..
61
………………………………… ………..
62
