AskSia

Plus

The reason your head feels like it jerks backward when pulling away from a sto...

May 9, 2024

The reason your head feels like it jerks backward when pulling away from a stop sign is best explained by Newton's First Law. Select one: True False

Solution

Newton's First Law, also known as the Law of Inertia, states that an object at rest stays at rest and an object in motion stays in motion with the same velocity unless acted upon by an external force

When a car pulls away from a stop sign, the car accelerates forward. However, your head, which was initially at rest, tends to remain at rest due to inertia

It is the car's seat that pushes against your back, causing your body to accelerate forward. Since your head is not directly acted upon by the same force, it lags behind momentarily before the muscles in your neck provide the force to accelerate it forward

This sensation of the head jerking backward is due to the inertia of the head resisting the forward acceleration of the car, which is consistent with Newton's First Law

Answer

True

Key Concept

Newton's First Law (Law of Inertia): An object at rest stays at rest, and an object in motion stays in motion with the same velocity unless acted upon by an external force.

Explanation

The sensation of the head jerking backward when a car accelerates from a stop is due to the inertia of the head, which is consistent with Newton's First Law.

An airplane is flying in level flight with constant velocity. The forward "thrust" force acting on the airplane is greater than the "drag" force acting in the opposite direction. Select one: True False

Solution

Apply Newton's First Law:

\sum F = 0

for an object moving with constant velocity

If the airplane is in level flight at constant velocity, the net force must be zero

Therefore, the "thrust" force must be equal to the "drag" force to maintain constant velocity

Answer

False

Key Concept

Newton's First Law (Law of Inertia): An object at rest stays at rest, and an object in motion stays in motion with the same velocity unless acted upon by an external force. Equation:

\sum F = 0

(Net force is zero)

Explanation

Since the airplane is flying with constant velocity, the net force acting on it must be zero, which means the thrust force must be equal to the drag force, not greater.

The force that propels you forward as you walk across the floor is the force that is exerted by the floor itself. Select one: True False

Solution

Apply Newton's Third Law:

F_{\text{action}} = -F_{\text{reaction}}

When you walk, your foot pushes backward on the floor. According to Newton's Third Law, the floor pushes forward on your foot with an equal and opposite force

This forward force from the floor propels you forward

Answer

True

Key Concept

Newton's Third Law: For every action, there is an equal and opposite reaction. Equation:

F_{\text{action}} = -F_{\text{reaction}}

(Action and reaction forces are equal and opposite)

Explanation

The force that propels you forward while walking is indeed the reaction force exerted by the floor in response to the action force applied by your foot.

If two forces that are identical in strength but exactly opposite in direction act on the same object, that object must necessarily be motionless. Select one: True False

Solution

Consider Newton's First Law, which states that an object will remain at rest or in uniform motion unless acted upon by a net external force

Apply the concept of net force:

\sum F = 0

when forces are equal and opposite

Conclude that the object does not necessarily have to be motionless; it could also be moving at constant velocity

Answer

False

Key Concept

Newton's First Law (Law of Inertia): An object at rest stays at rest, and an object in motion stays in motion with the same velocity unless acted upon by an external force. Equation:

\sum F = 0

(Net force is zero)

Explanation

The statement is false because if the net force is zero, the object could either be at rest or moving with a constant velocity. The forces being equal and opposite only implies that there is no acceleration, not that the object is motionless.

A child sits on a toboggan and slides down a hill with a particular acceleration. If another child joins the first one on the toboggan, they will slide down the hill with the same acceleration. Select one: True False

Solution

Consider Newton's Second Law:

F = ma

The net force on the toboggan is the component of gravitational force along the hill:

F_{\text{net}} = mg\sin(\theta)

, where

\theta

is the angle of the hill,

m

is the mass, and

g

is the acceleration due to gravity

The acceleration of the toboggan is given by:

a = \frac{F_{\text{net}}}{m} = \frac{mg\sin(\theta)}{m} = g\sin(\theta)

Adding another child increases the mass of the system (

m

becomes

m + m_{\text{child}}

), but the net force also increases proportionally, so the acceleration

a

remains the same

Answer

True

Key Concept

Newton's Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Equation:

F = ma

(Net force equals mass times acceleration)

Explanation

Since the net force and mass increase proportionally when another child joins the toboggan, the acceleration due to gravity remains constant, as it is independent of the mass of the toboggan and its occupants.

If the vector sum of all forces acting on an object is precisely zero, the object could still be moving. Select one: True False

Solution

Consider Newton's First Law of Motion, which states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force

If the vector sum of all forces acting on an object is zero, this means that the net force (

\sum F

) is zero. According to Newton's First Law, the object will not change its state of motion

Therefore, if the object was initially at rest, it will remain at rest. If it was moving, it will continue to move at a constant velocity in a straight line

Answer

True

Key Concept

Newton's First Law (Law of Inertia): An object at rest stays at rest, and an object in motion stays in motion with the same velocity unless acted upon by an external force. Equation:

\sum F = 0

(Net force is zero)

Explanation

The object could indeed still be moving if the vector sum of all forces acting on it is zero, as it would continue in its state of motion according to Newton's First Law.

When drawing a proper free-body diagram, all forces, including the net force acting on the object, must be clearly indicated. Select one: True False

Solution

A free-body diagram is a visual representation used to analyze the forces acting on an object

The diagram should include all the external forces acting on the object, but not the net force

The net force is the resultant of all the forces and is not shown as a separate vector in the diagram

Instead, the net force can be calculated from the diagram by vector addition of all the individual forces

Answer

False

Key Concept

Free Body Diagrams: Free body diagrams are used to analyze forces acting on an object. They show all forces acting on an object and their directions. The net force is not depicted as a vector in the diagram but is determined by the vector sum of all individual forces.

Explanation

In a free-body diagram, each force is represented by a vector. The net force is the vector sum of these forces and is calculated from them, not drawn as an individual vector.

A person pulls on one end of a rope whose other end is firmly tied to a sturdy pole. The force exerted by the person is not quite strong enough to break the rope. If the end is then untied from the pole and two people pull on opposite ends, each with a force identical to the person in the first case, the rope may break. Select one: True False

Solution

Consider the scenario where one person pulls the rope with a force that is not strong enough to break the rope

When two people pull on opposite ends with the same force, the total force on the rope is doubled

If the rope was close to its breaking point with one person pulling, doubling the force would likely exceed the rope's tensile strength, causing it to break

Answer

True

Key Concept

Tension: Tension is the force transmitted through a string, rope, or cable when it is pulled tight by forces acting from opposite ends. The total tension in the rope is the sum of the forces applied at both ends.

Explanation

Since each person is applying a force equal to the one that almost broke the rope when it was tied to the pole, the combined force is likely to be greater than the rope can withstand, leading to the rope breaking.

Two people pushing an object against friction across a surface will result in twice the acceleration than if only one person pushes. Assume that the object slides in both cases and that both people push with the same force. Select one: True False

Solution

Consider Newton's Second Law:

F = ma

If one person pushes with force

F

, two people push with total force

2F

The acceleration with one person is

a = \frac{F}{m}

, with two people it is

a' = \frac{2F}{m} = 2a

Friction is constant in both cases, so it does not affect the comparison of acceleration

Answer

True

Key Concept

Newton's Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Equation:

F = ma

(Net force equals mass times acceleration)

Explanation

If both people push with the same force, the total force applied to the object is doubled, which according to Newton's Second Law, would result in doubling the acceleration, assuming mass remains constant and friction does not change.

Two people pushing an object across a frictionless surface will result in twice the acceleration than if only one person pushes. Assume the object slides in both cases and that both people push with the same force. Select one: True False

Solution

Apply Newton's Second Law:

F = ma

to the scenario with one person pushing

If one person applies a force

F

, the acceleration

a_1

is given by

a_1 = \frac{F}{m}

, where

m

is the mass of the object

Apply Newton's Second Law to the scenario with two people pushing

If two people apply the same force

F

each, the total force is

2F

. The acceleration

a_2

is given by

a_2 = \frac{2F}{m} = 2\left(\frac{F}{m}\right) = 2a_1

Answer

True

Key Concept

Newton's Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Equation:

F = ma

(Net force equals mass times acceleration)

Explanation

When two people push the object with the same force as one person, the total force doubles, resulting in double the acceleration, assuming the mass of the object remains constant.

A squirrel with an armful of nuts is sliding helplessly across the flat, icy roof, getting dangerously close to the edge. He understands Newton’s Third Law, and is able to save himself. Explain how he does it. (6 marks) [K/2; T/1.5; C/1.5; A/1]

Solution

Understand the scenario: A squirrel is sliding on an icy roof, which implies there is little to no friction. The squirrel is approaching the edge and must use a force to change its state of motion

Apply Newton's Third Law: The squirrel can throw the nuts it is carrying in the direction opposite to the sliding motion. By doing so, it exerts a force on the nuts

Action and Reaction Forces: According to Newton's Third Law, the nuts will exert an equal and opposite force on the squirrel. This is the reaction force

Resulting Motion: The reaction force acting on the squirrel will be in the direction opposite to its initial motion, which can slow down or stop the squirrel, preventing it from sliding off the roof

Quantitative Analysis: If we assume the mass of the nuts is

m_n

and the squirrel throws them with a velocity

v_n

, the momentum imparted to the nuts is

p = m_n v_n

. By conservation of momentum, the squirrel will gain an equal and opposite momentum, which can be enough to stop it

Answer

The squirrel can save itself by throwing the nuts in the direction it is sliding from. By exerting a force on the nuts, it experiences an equal and opposite reaction force that can stop its sliding motion, thus preventing it from falling off the roof.

Key Concept

Newton's Third Law: For every action, there is an equal and opposite reaction. Equation:

F_{\text{action}} = -F_{\text{reaction}}

Explanation

The squirrel uses Newton's Third Law by throwing the nuts to create an action force, which in turn produces an equal and opposite reaction force on itself, changing its state of motion and allowing it to stop before reaching the edge of the roof.

Why does the gravitational field strength at the surface of Earth vary from location to location? (4 marks) [K/2; T/2]

Solution

The gravitational field strength, denoted by

g

, is influenced by the mass of the Earth and the distance from the Earth's center. The formula for gravitational field strength is

g = \frac{GM}{r^2}

, where

G

is the gravitational constant,

M

is the mass of the Earth, and

r

is the distance from the center of the Earth to the point where

g

is being measured

The Earth is not a perfect sphere; it is an oblate spheroid, which means it is slightly flattened at the poles and bulges at the equator. This causes variations in the value of

r

, the distance from the Earth's center, which affects

g

Additionally, the distribution of mass within the Earth is not uniform. Variations in Earth's density, such as mountain ranges, large bodies of water, or other geological structures, can locally affect the gravitational field strength

Earth's rotation also affects the gravitational field strength. Centrifugal force due to the Earth's rotation is greatest at the equator and zero at the poles. This force effectively reduces the gravitational pull experienced by objects at the equator, leading to a slightly lower value of

g

there

Answer

The gravitational field strength at the surface of Earth varies due to the oblate spheroid shape of the Earth, the non-uniform distribution of Earth's mass, and the centrifugal force resulting from Earth's rotation.

Key Concept

The gravitational field strength at a point is given by the formula

g = \frac{GM}{r^2}

, where

G

is the gravitational constant,

M

is the mass of the attracting body, and

r

is the distance from the center of the mass to the point in question. The Earth's shape, mass distribution, and rotation all contribute to variations in

g

Explanation

The variation in gravitational field strength is due to the Earth's oblate shape, inhomogeneous mass distribution, and the centrifugal force from its rotation, which all cause changes in the distance

r

and the effective mass that influences the gravitational pull at different locations on Earth's surface.

Clearly distinguish between the terms "mass" and "weight." (4 marks) [K/2; T/1.5; C/0.5]

Solution

Define mass: Mass is a measure of the amount of matter in an object and is a scalar quantity. It is an intrinsic property of the object and does not change regardless of its location. Mass is measured in kilograms (kg) in the International System of Units (SI)

Define weight: Weight is the force exerted on an object due to gravity. It is a vector quantity, which means it has both magnitude and direction. Weight can be calculated using the equation

W = mg

where

W

is weight,

m

is mass, and

g

is the acceleration due to gravity. Weight is measured in newtons (N) in the SI system

Contrast mass and weight: While mass is constant for an object, weight can change depending on the local gravitational field strength. For example, an object will weigh less on the Moon than on Earth due to the Moon's weaker gravitational pull

Practical implications: Understanding the difference between mass and weight is important for scenarios such as calculating the gravitational force on an object (weight) or understanding the resistance to acceleration (inertia) due to its mass

Answer

Mass is the measure of matter in an object, constant and measured in kg. Weight is the gravitational force on an object, variable depending on gravity, and measured in N.

Key Concept

Mass is a scalar quantity indicating the amount of matter in an object, while weight is a vector quantity representing the gravitational force acting on that mass.

Explanation

Mass remains constant regardless of location, while weight can change with the local acceleration due to gravity. The distinction is crucial in physics to understand how objects will behave under different gravitational conditions.

Distinguish between the terms "static" and "kinetic" friction. (5 marks) [K/1; T/1; C/1; A/2]

Solution

Define static friction: Static friction is the force that resists the initiation of sliding motion between two surfaces that are in contact and at rest relative to each other

Define kinetic friction: Kinetic friction is the force that opposes the relative sliding motion between two surfaces that are in contact and moving relative to each other

Static friction equation: The maximum static friction force can be calculated using the equation

f_{\text{static max}} = \mu_s N

, where

\mu_s

is the coefficient of static friction and

N

is the normal force

Kinetic friction equation: The kinetic friction force is calculated using the equation

f_{\text{kinetic}} = \mu_k N

, where

\mu_k

is the coefficient of kinetic friction and

N

is the normal force

Discuss the coefficients: The coefficient of static friction is typically higher than the coefficient of kinetic friction for a given pair of surfaces, which means it usually takes more force to start the motion than to maintain it

Answer

Static friction is the force that prevents two surfaces from sliding past each other and is greater than kinetic friction, which is the force that opposes the motion once it has started. The maximum static friction force is given by

f_{\text{static max}} = \mu_s N

, and the kinetic friction force is given by

f_{\text{kinetic}} = \mu_k N

, where

\mu_s

and

\mu_k

are the coefficients of static and kinetic friction, respectively, and

N

is the normal force.

Key Concept

Static and kinetic friction: Static friction acts on stationary objects preventing the onset of motion, while kinetic friction acts on moving objects opposing their motion. The coefficients of static and kinetic friction are material-specific and determine the magnitude of the frictional forces.

Explanation

Provide examples that illustrate that friction is sometimes desirable and sometimes undesirable. (3 marks) [ T/2; C/0.5, A/0.5]

Solution

Desirable friction: Braking systems in vehicles use friction to slow down or stop the motion of the car. The friction between the brake pads and the wheels converts kinetic energy into thermal energy, allowing the vehicle to come to a halt

Undesirable friction: In mechanical systems like engines, friction between moving parts can lead to energy loss as heat, reducing efficiency. This is why lubricants are used to minimize friction and wear between components

Desirable friction: Friction between our shoes and the ground allows us to walk without slipping. This frictional force provides the necessary grip to push against the ground and move forward

Answer

Examples of desirable friction include braking systems in vehicles and the grip between shoes and the ground. Examples of undesirable friction include energy loss in engines due to friction between moving parts.

Key Concept

Friction is a force that opposes relative motion between surfaces in contact. It can be either desirable or undesirable depending on the situation. Kinetic friction is given by the equation

f_{\text{kinetic}} = \mu_k N

where

\mu_k

is the coefficient of kinetic friction and

N

is the normal force.

Explanation

Friction is essential for many everyday activities, such as walking and driving, where it prevents slipping and enables controlled motion. However, in mechanical systems, friction can lead to energy loss and wear, which is why it is often undesirable in those contexts.

A cart with a mass of 2.0 kg is pulled across a level desk by a horizontal force of 4.0 N. If the coefficient of kinetic friction is 0.12, what is the acceleration of the cart? (6 marks) [K/1; T/1; C/2; A/2]

Solution

Calculate the force of kinetic friction using the coefficient of kinetic friction and the normal force. The normal force is equal to the gravitational force on the cart, which is the product of the mass and the acceleration due to gravity (

g = 9.8 \, m/s^2

). The force of kinetic friction (

f_{\text{kinetic}}

) is then:

f_{\text{kinetic}} = \mu_k \cdot m \cdot g

f_{\text{kinetic}} = 0.12 \cdot 2.0 \, kg \cdot 9.8 \, m/s^2

f_{\text{kinetic}} = 2.352 \, N

Determine the net force acting on the cart. The net force (

F_{\text{net}}

) is the applied force minus the force of kinetic friction:

F_{\text{net}} = F_{\text{applied}} - f_{\text{kinetic}}

F_{\text{net}} = 4.0 \, N - 2.352 \, N

F_{\text{net}} = 1.648 \, N

Use Newton's Second Law to calculate the acceleration (

a

) of the cart.

F = ma

a = \frac{F}{m}

a = \frac{1.648 \, N}{2.0 \, kg}

a = 0.824 \, m/s^2

Answer

The acceleration of the cart is 0.824 m/s^2

Key Concept

Newton's Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Equation:

F = ma

(Net force equals mass times acceleration)

Explanation

The acceleration was found by first calculating the force of kinetic friction, then determining the net force acting on the cart, and finally applying Newton's Second Law to find the acceleration

How much force would be required to start a 1.0-kg object sliding along a horizontal surface if the coefficient of starting friction is 0.20? (4 marks) [K/0.5; T/2; C/1; A/0.5]

Solution

Identify the forces acting on the object: The only horizontal force acting on the object when it starts sliding is the force of static friction, which we need to overcome to start the motion

Calculate the normal force (

F_{\text{normal}}

): Since the object is on a horizontal surface and not accelerating vertically, the normal force is equal to the gravitational force on the object.

F_{\text{normal}} = mg

where

m

is the mass of the object and

g

is the acceleration due to gravity (approximately

9.8 \, \text{m/s}^2

)

Calculate the maximum static friction force (

f_{\text{static,max}}

): The maximum static friction force is given by the product of the coefficient of static friction (

\mu_s

) and the normal force (

F_{\text{normal}}

f_{\text{static,max}} = \mu_s F_{\text{normal}}

Determine the force required to overcome static friction: The force required to start the object sliding must be equal to or greater than the maximum static friction force.

F_{\text{required}} = f_{\text{static,max}}

Substitute the values and calculate

F_{\text{required}}

F_{\text{required}} = \mu_s mg

F_{\text{required}} = 0.20 \times 1.0 \, \text{kg} \times 9.8 \, \text{m/s}^2

F_{\text{required}} = 1.96 \, \text{N}

Answer

1.96 N

Key Concept

Static Friction: Static friction is the force that must be overcome to start the motion of an object resting on a surface. It is calculated using the coefficient of static friction and the normal force. The equation for the maximum static friction force is

f_{\text{static,max}} = \mu_s F_{\text{normal}}

Explanation

To start the object sliding, a force equal to or greater than the maximum static friction force must be applied. In this case, the force required is 1.96 N.

If a 7.2 N force is required to accelerate a 3.4-kg object along a horizontal surface at a rate of 1.6 m/s2, what is the frictional resistance that is acting? (6 marks) [K/1; T/1; C/1, A/3]

Solution

Identify the known values: mass

m = 3.4 \, \text{kg}

, acceleration

a = 1.6 \, \text{m/s}^2

, and applied force

F_{\text{applied}} = 7.2 \, \text{N}

Apply Newton's Second Law to find the net force:

F_{\text{net}} = ma

Calculate the net force using the mass and acceleration:

F_{\text{net}} = 3.4 \, \text{kg} \times 1.6 \, \text{m/s}^2 = 5.44 \, \text{N}

Determine the frictional force: Since the applied force is used to overcome friction and accelerate the object, the frictional force

f_{\text{friction}}

can be found by subtracting the net force from the applied force:

f_{\text{friction}} = F_{\text{applied}} - F_{\text{net}}

Calculate the frictional resistance:

f_{\text{friction}} = 7.2 \, \text{N} - 5.44 \, \text{N} = 1.76 \, \text{N}

Answer

The frictional resistance acting on the object is 1.76 N.

Key Concept

Newton's Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Equation:

F = ma

(Net force equals mass times acceleration)

Explanation

The frictional resistance is calculated by subtracting the net force (which is the product of mass and acceleration) from the applied force. This gives us the force that opposes the motion, which is the frictional force.

A wagon of mass 2.4 kg is pushed along the ground at 1.2 m/s2 against a frictional force of 1.22 N. What is the applied force that is acting? Draw a free-body diagram. (2 marks) [T/1.5; C/0.5]

Solution

Identify the known values: mass (m) = 2.4 kg, acceleration (a) = 1.2 m/s², and frictional force (

f_{\text{friction}}

) = 1.22 N

Calculate the net force (

F_{\text{net}}

) required to accelerate the wagon using Newton's Second Law:

F_{\text{net}} = ma

Substitute the known values into the equation:

F_{\text{net}} = 2.4 \text{ kg} \times 1.2 \text{ m/s}^2 = 2.88 \text{ N}

Determine the total applied force (

F_{\text{applied}}

) by adding the frictional force to the net force, since the applied force must overcome both the inertia of the wagon and the frictional force:

F_{\text{applied}} = F_{\text{net}} + f_{\text{friction}}

Calculate the applied force:

F_{\text{applied}} = 2.88 \text{ N} + 1.22 \text{ N} = 4.10 \text{ N}

Draw a free-body diagram showing the forces acting on the wagon:

- An arrow pointing to the right representing the applied force (

F_{\text{applied}}

). - An arrow pointing to the left representing the frictional force (

f_{\text{friction}}

). - An arrow pointing downward representing the gravitational force (

F_{\text{gravity}} = mg

). - An arrow pointing upward representing the normal force (

F_{\text{normal}}

), which is equal in magnitude and opposite in direction to the gravitational force.

Answer

The applied force acting on the wagon is 4.10 N.

Key Concept

Newton's Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Equation:

F = ma

(Net force equals mass times acceleration)

Explanation

To find the applied force, we used Newton's Second Law to calculate the net force needed to accelerate the wagon and then added the frictional force to determine the total applied force.