Effects Of Forces

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レッスンノート

Resultant Forces

A force is a push or pull that acts on an object due to interaction with another object.
Forces can change an object's speed, direction, shape, or size.
A resultant force is a single force that represents the combined effect of all forces acting on an object.
Balanced forces are equal in magnitude and opposite in direction; they cancel out, giving zero resultant force.
Unbalanced forces produce a non-zero resultant force, causing a change in motion.
To calculate resultant force, assign positive/negative signs to directions and sum the forces.

Forces acting on a book resting on a table

Newton's First Law

Newton's First Law: An object remains at rest or moves with constant velocity unless acted on by a resultant force.
Constant velocity means no change in speed and no change in direction.
If resultant force is zero, the object is either stationary or moving at constant velocity.
Example: A car moving at constant speed in a straight line has balanced driving and frictional forces.
The Moon orbits Earth at constant speed but changes direction, so it does not obey Newton's First Law (it has a resultant force).

Examples of Newton's First Law

Newton's Second Law

Newton's Second Law: The acceleration of an object is proportional to the resultant force and inversely proportional to its mass.
Equation: F = ma (force in N, mass in kg, acceleration in m/s²).
Acceleration occurs in the same direction as the resultant force.
For a given force, a larger mass gives a smaller acceleration.
Example: A 900 kg car accelerating at 9 m/s² requires a force of 8100 N.

Examples of resultant forces causing acceleration in a baseball and a lawnmower.

Investigating Force & Extension

Aim: Investigate the relationship between force and extension of a spring.
Independent variable: Force (weight added). Dependent variable: Extension.
Use a clamp stand, spring, masses, ruler, and pointer to measure extension.
Calculate extension: extension = final length – original length.
Plot a graph of force vs. extension; a straight line through origin shows direct proportionality (Hooke's Law).
Take readings at eye level to avoid parallax error; repeat for reliability.

Equipment for investigating the extension of a spring

Hooke's Law

Hooke's Law: The extension of an elastic object is directly proportional to the force applied, up to the limit of proportionality.
Equation: F = kx, where k is the spring constant (N/m) and x is extension (m).
Spring constant k = F/x; a high k means a stiff spring.
On a force-extension graph, the gradient of the linear region equals the spring constant.
Beyond the limit of proportionality, the graph curves and Hooke's Law no longer applies.

Force-extension graph for a spring

Circular Motion

In circular motion, the velocity changes because direction changes, even if speed is constant.
A force acting perpendicular to motion causes the object to travel in a circle.
The force is always directed toward the centre of the circle (centripetal force).
Factors affecting required force: mass (greater mass needs more force), speed (faster needs more force), radius (smaller radius needs more force).

Circular motion of the International Space Station

Friction

Friction opposes motion and causes heating (energy transfer).
Solid friction arises from surface imperfections; can be reduced by lubrication or smoothing.
Drag (air resistance) is friction in fluids; it slows objects and heats them.
Air resistance can be reduced by streamlining the object's shape.

Air resistance acting on a rocket's return module as it re-enters Earth's atmosphere.

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練習問題

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1.Which of the following is the correct definition of a force?
Easy
- AA push or a pull that acts on an object due to interaction with another object
- BA measure of the amount of matter in an object
- CThe rate of change of velocity of an object
- DThe energy transferred when an object is moved
2.What is a resultant force?
Easy
- AA single force that describes all of the forces operating on a body
- BThe largest force acting on an object
- CThe sum of all forces ignoring direction
- DThe force that remains when all other forces are removed
3.A book is at rest on a table. Which statement about the forces acting on the book is correct?
Easy
- AThe weight of the book and the normal contact force are balanced
- BThe weight of the book is greater than the normal contact force
- CThe normal contact force is greater than the weight of the book
- DThere is no resultant force because no forces are acting on the book
4.A car is moving at a constant velocity. The driving force from the engine is 3 kN. What is the frictional force acting on the car?
Medium
- A3 kN
- B0 kN
- C6 kN
- D1.5 kN
5.The Moon orbits the Earth at a constant speed. Which statement about the Moon's motion is correct?
Medium
- AThe Moon is accelerating because its direction is changing
- BThe Moon is not accelerating because its speed is constant
- CThe Moon is not accelerating because no resultant force acts on it
- DThe Moon is accelerating only when its speed changes
6.Which of the following is NOT an effect that a force can have on an object?
Easy
- AChange the mass of the object
- BChange the speed of the object
- CChange the direction of the object
- DChange the shape of the object
7.A 2 kg object accelerates at 3 m/s². What is the resultant force acting on it?
Easy
- A6 N
- B1.5 N
- C5 N
- D0.67 N
8.A spring has an unstretched length of 5 cm. When a 2 N weight is hung from it, its length becomes 9 cm. What is the spring constant?
Medium
- A50 N/m
- B0.5 N/m
- C0.22 N/m
- D22.2 N/m

もっと問題

9.What is the unit of the spring constant?
Easy
- AN/m
- BN
- CN·m
- Dm/N
10.Which of the following is true about an object moving in a circle at constant speed?
Medium
- AThe object is accelerating because its direction changes
- BThe object has no acceleration because its speed is constant
- CThe resultant force on the object is zero
- DThe object moves in a straight line if no force acts on it
11.Friction in solids is caused by:
Easy
- AImperfections in the surfaces of objects moving over one another
- BThe weight of the objects
- CThe speed of the objects
- DThe temperature of the surroundings
12.Which of the following would reduce friction between two solid surfaces?
Easy
- ALubricating the surfaces
- BIncreasing the roughness of the surfaces
- CIncreasing the force pressing them together
- DIncreasing the area of contact
13.A student measures the unstretched length of a spring as 2.1 cm. When a load of 1.0 N is hung on the spring, the stretched length is 6.3 cm. What is the extension of the spring?
Easy
- A4.2 cm
- B6.3 cm
- C8.4 cm
- D2.1 cm
14.In an experiment to investigate the stretching of a spring, a student records the following data: Load = 2.0 N, stretched length = 10.5 cm, unstretched length = 2.1 cm. What is the spring constant?
Medium
- A0.24 N/cm
- B4.2 N/cm
- C0.19 N/cm
- D2.0 N/cm
15.A student determines the spring constant of a spring using two methods. In Method 1, a 300 g mass (weight 3.0 N) produces an extension of 23 mm. In Method 2, the mass oscillates and the period squared is 0.16 s². Using k = 0.040×m / T² with m = 0.300 kg, what is the spring constant from Method 2?
Hard
- A0.075 N/mm
- B0.13 N/mm
- C0.075 N/m
- D0.13 N/m
16.In a force-extension experiment, a student plots load (L) against extension (e). The graph is a straight line through the origin. Which statement is correct?
Medium
- Ae is directly proportional to L
- BL is inversely proportional to e
- CThe gradient equals the spring constant
- DThe limit of proportionality has been exceeded
17.A student measures the unstretched length of a spring as 2.1 cm. Loads are added and the stretched lengths are recorded. For a load of 3.0 N, the stretched length is 14.7 cm. What is the extension?
Easy
- A12.6 cm
- B14.7 cm
- C16.8 cm
- D2.1 cm
18.A student gives the weight of a load as 4.532 N from an experiment using a spring and a metre rule. Why is this not a suitable number of significant figures?
Medium
- AThe metre rule can only be read to the nearest mm, so the weight should have at most 3 significant figures
- BThe spring constant has only 2 significant figures
- CThe weight should be given to the nearest 0.1 N
- DThe number of significant figures is too low
19.In an experiment to find the spring constant, a student uses a 300 g mass and measures an extension of 23 mm. The force is 3.0 N. What is the spring constant in N/m?
Medium
- A130 N/m
- B0.13 N/m
- C7.7 N/m
- D13000 N/m
20.A student repeats an experiment to measure the extension of a spring for different loads. Which action would improve the reliability of the results?
Easy
- ARepeat the experiment several times and calculate the average extension for each load
- BUse a different spring each time
- CMeasure the length only once for each load
- DUse larger loads to get bigger extensions
21.A student investigates the stretching of a spring. The unstretched length is measured as 1.5 cm. With a load of 1.0 N, the new length is 2.2 cm. What is the extension?
Easy
- A0.7 cm
- B1.5 cm
- C2.2 cm
- D3.7 cm
22.A student suspends a load of 5.0 N from a spring and measures the new length as 6.3 cm. The unstretched length is 1.5 cm. What is the spring constant to two significant figures?
Medium
- A1.0 N/cm
- B1.04 N/cm
- C0.96 N/cm
- D0.79 N/cm
23.In a force-extension experiment, a student uses a set square to read the metre rule. What is the purpose of using a set square?
Easy
- ATo avoid parallax error by ensuring the eye is at the same level as the reading
- BTo measure the diameter of the spring
- CTo clamp the ruler firmly
- DTo mark the position of the pointer
24.A student uses a spring to determine the weight of an object X. The unstretched length of the spring is 2.1 cm. When X is suspended, the stretched length is 11.4 cm. The spring constant is known to be 0.25 N/cm. What is the weight of object X?
Medium
- A2.3 N
- B2.9 N
- C0.5 N
- D1.1 N
25.A student determines the spring constant of a spring using two methods. In Method 1, a 300 g mass (weight 3.0 N) produces an extension of 23 mm. In Method 2, the mass is set oscillating and the time for 10 oscillations is 6.0 s. Using T = 0.6 s and the equation k = 0.040 m/T², what is the spring constant from Method 2? (m = 0.300 kg)
Hard
- A0.033 N/mm
- B0.020 N/mm
- C0.050 N/mm
- D0.040 N/mm
26.A student wants to investigate the effect of air resistance on the swing of a pendulum. Which of the following is a key variable to control?
Medium
- AThe length of the pendulum.
- BThe shape of the pendulum bob.
- CThe amplitude of the swing.
- DAll of the above.
27.In an experiment to investigate the force required to break beams, all beams have the same cross-section. Which variable should be changed to investigate how length affects the breaking force?
Easy
- AThe length of the beam.
- BThe ratio of sand to cement.
- CThe cross-sectional area.
- DThe type of support.
28.A student uses a spring to determine the weight of an object X. The unstretched length of the spring is 2.1 cm. When X is suspended, the stretched length is 11.4 cm. Earlier readings for the same spring: | Load (N) | Extension (cm) | |---|---| | 1.0 | 4.2 | | 2.0 | 8.4 | | 3.0 | 12.6 | What is the weight of object X?
Medium
- A2.2 N
- B2.7 N
- C2.0 N
- D3.0 N
29.A student determines the spring constant of a spring using two methods. In Method 1, a 300 g mass (weight 3.0 N) produces an extension of 23 mm. In Method 2, the spring constant is calculated from oscillations as 0.13 N/mm. Are the two values within experimental accuracy?
Medium
- AYes, because Method 1 gives k = 3.0/23 = 0.130 N/mm, which is the same as 0.13 N/mm.
- BNo, because Method 1 gives k = 23/3.0 = 7.67 N/mm, which is different.
- CYes, because both methods give the same extension.
- DNo, because the mass is different in each method.
30.A car of mass 900 kg accelerates from 0 to 27 m/s in 3 seconds. What is the resultant force acting on the car?
Medium
- A8100 N
- B300 N
- C24300 N
- D2700 N
31.A spring has a spring constant of 100 N/m. What force is needed to extend it by 0.05 m?
Easy
- A5 N
- B0.5 N
- C2000 N
- D20 N
32.An object of mass 2 kg is moving in a circular path of radius 5 m at a constant speed of 10 m/s. Which statement about the forces acting on it is correct?
Medium
- AA resultant force acts towards the centre of the circle.
- BNo resultant force acts because the speed is constant.
- CA resultant force acts away from the centre of the circle.
- DThe resultant force is zero because the object is in equilibrium.
33.A student determines the spring constant of a spring using two methods. In Method 1, a 300 g mass (weight 3.0 N) produces an extension of 23 mm. In Method 2, the time for 10 oscillations is measured as 2.0 s. Using k = 0.040×m / T² with m = 0.300 kg and T = 0.20 s, the calculated k is 0.30 N/mm. Which statement explains why the two values might differ?
Hard
- AMethod 2 is affected by the mass of the spring, which is ignored.
- BThe extension in Method 1 is measured incorrectly due to parallax error.
- CThe spring constant is different for static and dynamic methods.
- DThe mass used in Method 2 should be 300 g including the hanger.
34.A force can change the shape of an object.
Easy
True or false?
35.An object moving with constant velocity has a resultant force acting on it.
Easy
True or false?
36.An object moving in a circle at constant speed has a resultant force acting on it.
Medium
True or false?
37.Which of the following can reduce friction between two solid surfaces? (Select all that apply)
Medium
- ALubricating the surfaces
- BSmoothing the surfaces
- CIncreasing the force pressing them together
- DMaking the surfaces rougher
38.Match each effect of a force with the correct example.
Easy
- Change speed
- Change direction
- Change shape
- A spring compresses
- A car accelerates
- A comet orbits the Sun
39.Arrange the steps for calculating the resultant force in the correct order.
Medium
- Assign positive direction to one side
- Add all forces with sign
- State magnitude and direction of resultant
- Identify all forces acting on object
40.Which of the following are effects of friction? (Select all that apply)
Easy
- AIt slows down moving objects
- BIt increases the temperature of objects
- CIt causes objects to accelerate
- DIt opposes motion
41.In a force-extension experiment, a student plots load on the y-axis and extension on the x-axis. The graph is a straight line through the origin. What does the gradient represent?
Medium
- AThe spring constant
- BThe reciprocal of the spring constant
- CThe extension per unit load
- DThe work done
42.Complete the sentence.
Easy
Newton's first law states that objects will remain at rest, or move with a constant ____ unless acted on by a resultant force.
43.A spring has a spring constant of 200 N/m. What force is needed to stretch it by 0.05 m?
Easy
44.Complete the sentence about Newton's first law.
Easy
An object will remain at rest or move with ____ unless acted on by a resultant force.
45.Explain why a car moving at a constant speed in a straight line has no resultant force acting on it.
Medium
46.A spring has a spring constant of 200 N/m. What force is needed to stretch it by 0.05 m?
Easy
- A10 N
- B11 N
- C9 N
- D12 N

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