Question 1:

The symbol μ_s represents the coefficient of static friction. This dimensionless quantity describes the ratio of the maximum force of static friction (F_s) to the normal force (N) pressing two surfaces together. The formula is:

F_s ≤μ_s N

The coefficient of static friction (μ_s) is a measure of how much friction exists between two surfaces that are not moving relative to each other.

The correct answer is B. the coefficient of static friction.

*These A.I. responses have been individually checked to ensure they match the accepted answer, but explanations may still be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
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Question 2:

The coefficient of dynamic (or kinetic) friction, μ_d, represents the ratio between the force of kinetic friction and the normal force. The formula is:

F_d = μ_d N

Where:

• F_d is the force of dynamic friction.
• μ_d is the coefficient of dynamic friction.
• N is the normal force.

Therefore, if μ_d =0.5, it means that the force of friction is half the size of the normal force, or F_d =0.5×N. This relationship holds true regardless of the object's weight, driving force, or air resistance. The normal force is the perpendicular force exerted by a surface on an object in contact with it.

The correct answer is C. the normal force (reaction) of the surface on the object.
​

*These A.I. responses have been individually checked to ensure they match the accepted answer, but explanations may still be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
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Question 3:

Normal Force on the book
The book is resting on a horizontal surface, which means there are no vertical forces other than its weight and the normal force from the surface. Since the book is not accelerating vertically, the normal force must be equal in magnitude to its weight.

Weight (W) is calculated using the formula W=mg.

m=1.0 kg

Use g≈10 N/kg for simplicity.

W=1.0 kg×10 N/kg
=10 N.

Therefore, the Normal Force (N) is approximately 10 N. This corresponds to answer C.

*These A.I. responses have been individually checked to ensure they match the accepted answer, but explanations may still be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
Grade Gorilla uses Gemini, Deepseek and a range of other A.I. chatbots to generate the saved responses. Some answers have had human intervention for clarity or where the A.I. has not been able to answer the question.

Question 4:

Maximum frictional force
The maximum static frictional force (F_s,max) is calculated by multiplying the coefficient of static friction (μ_s) by the normal force (N).

F_s,max=μ_s ×N

μ_s =0.4

N=10 N

F_s,max=0.4×10 N=4 N.

This is the maximum force that can be applied before the book begins to slide.

This corresponds to answer D.

*These A.I. responses have been individually checked to ensure they match the accepted answer, but explanations may still be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
Grade Gorilla uses Gemini, Deepseek and a range of other A.I. chatbots to generate the saved responses. Some answers have had human intervention for clarity or where the A.I. has not been able to answer the question.

Question 5:

Forces on an inclined slope
When the horizontal surface is raised to form a slope, the normal force and the maximum static frictional force both change.

Normal Force: The normal force is always perpendicular to the surface. As the slope's angle (θ) increases, the component of the book's weight that is perpendicular to the surface decreases. The formula for the normal force on a slope is N=mgcosθ. Since cosθ decreases as θ increases from 0 to 90 degrees, the normal force also decreases.

Maximum Static Frictional Force: The maximum static frictional force is directly proportional to the normal force F_s,max=μ_s ×N. Since the normal force is decreasing as the slope is lifted, the maximum static frictional force also decreases.

This corresponds to answer A.

*These A.I. responses have been individually checked to ensure they match the accepted answer, but explanations may still be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
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Question 6:

The correct statement is C. The weight of water displaced is equal to the total weight of the boat.

Archimedes' Principle
This is a direct application of Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid that the object displaces. For an object to float, the buoyant force must be equal in magnitude to the object's total weight.

Weight of water displaced is the buoyant force.

The buoyant force must be equal to the total weight of the boat for it to float in equilibrium.

Here is a breakdown of the other options:

A and B are incorrect because they focus on the mass or weight of the portion of the boat that is underwater, not the total mass or weight. The principle applies to the entire object.

D is incorrect because the volume of water displaced is only equal to the volume of the part of the boat that is submerged below the waterline, not the total volume of the boat.

*These A.I. responses have been individually checked to ensure they match the accepted answer, but explanations may still be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
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Question 7:

The correct answer is D. 8 times larger, 8 times larger.

When the radius of a spherical object is doubled, both its weight and the buoyancy force acting on it increase by a factor of 8. This is because both forces are directly proportional to the volume of the sphere.

Weight (W)
The weight of the ball is given by the formula W=mg, where m is the mass and g is the acceleration due to gravity. The mass is the density of the aluminum (ρ) multiplied by the volume of the ball (V).

m=ρ x V

The volume of a sphere is given by the formula V= 4/3 πr³ Substituting the volume into the weight equation:

W=ρ ​4/3 πr³ . g

If the radius (r) is doubled to 2r, the new weight (W') will be:

W'=ρ ​4/3 π(2r)³ . g
W'=ρ ​4/3 π 8 r³ . g
W'=8W

The weight becomes 8 times larger.

Buoyancy Force (F_b)
According to Archimedes' Principle, the buoyancy force is equal to the weight of the displaced fluid. The volume of the displaced fluid is the same as the volume of the ball itself.

F_b=weight of displaced fluid=ρ ​4/3 πr³. g

If the radius (r) is doubled to 2r, the new buoyancy force F_b' will be:

F_b' =ρ ​4/3 π(2r)³ . g
F_b'=ρ ​4/3 π 8 r³ . g
F_b'= 8F_b

The buoyancy force also becomes 8 times larger.

*These A.I. responses have been individually checked to ensure they match the accepted answer, but explanations may still be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
Grade Gorilla uses Gemini, Deepseek and a range of other A.I. chatbots to generate the saved responses. Some answers have had human intervention for clarity or where the A.I. has not been able to answer the question.

Question 8:

Explanation
When the ball reaches terminal velocity, it means that its acceleration is zero. According to Newton's First Law of Motion, this occurs when the net force acting on the object is zero, i.e., all the forces are balanced.

The forces acting on the falling ball are:

• Weight (W): Acts downwards, caused by gravity.
• Buoyancy force (F_b): Acts upwards, caused by the displaced fluid.
• Viscous drag force (F_v): Acts upwards, caused by the resistance of the fluid.

For the forces to be balanced, the total upward force must be equal to the total downward force.

Downward force: W

Upward forces: F_b+F_v

Therefore, at terminal velocity, the sum of the upward forces equals the downward force:
W=F_b+F_v

The correct statement is A. The forces are balanced, and W = F_v + F_b.

*These A.I. responses have been individually checked to ensure they match the accepted answer, but explanations may still be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
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Question 9:

When the ball is at rest on the bottom of the cylinder, the forces on it are balanced. The downward force (the ball's weight) is equal to the sum of the upward forces (the buoyancy force and the normal force from the bottom of the cylinder).

Downward Force:
The only downward force is the ball's weight, W.
W=mg

Upward Forces:

The buoyant force (F_B) is the upward force exerted by the oil on the ball. According to Archimedes' principle, this force is equal to the weight of the fluid displaced by the ball.
F_B =weight of displaced oil=(density of oil)×(volume of ball)×g
F_B = ρ_oilV g
​

The normal force (F_N) is the force exerted by the bottom of the cylinder on the ball.

Equilibrium Equation:
Since the ball is not moving, the forces are in equilibrium:
Total Downward Force = Total Upward Force
W=F_B + F_N
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Solve for the Normal Force:
mg=ρ_oilV g ​+ F_N
​F_N = mg - ρ_oilV g
​
Factor out g:

​F_N = g (m - ρ_oilV)

The correct answer is C. F_N = g(m−ρ_oilV).
​

*These A.I. responses have been individually checked to ensure they match the accepted answer, but explanations may still be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
Grade Gorilla uses Gemini, Deepseek and a range of other A.I. chatbots to generate the saved responses. Some answers have had human intervention for clarity or where the A.I. has not been able to answer the question.

Question 10:

When a ball of the same radius but with 3 times the density is used, its terminal velocity increases. Here's why:

At terminal velocity, the downward force (weight, W) is balanced by the upward forces (buoyancy force, F_b
​
, and viscous drag force, F_v).
W=F_b+F_v

The buoyancy force (F_b) is dependent on the volume of the ball and the density of the fluid. Since the radius (and thus volume) of the ball is unchanged, the buoyancy force remains the same.

The weight (W) is given by W=mg, which can be written as W=ρVg. Since the density of the ball is 3 times greater and the volume (V) is the same, the weight is 3 times larger.

With a larger downward force and the same upward buoyancy force, a greater viscous drag force is required to achieve a balance and reach terminal velocity.

The viscous drag force (F_v) depends on the velocity of the ball. The exact relationship can vary, but for many objects falling at moderate speeds in a fluid like oil, drag is proportional to velocity (F_v∝v). Since a larger drag force is needed to balance the increased weight, the terminal velocity must increase.

W' =F_b + F_v'

3W=F_b + F_v'

Since W>F_b , the new drag force F_v' ) must be significantly larger than the old drag force (F_v ), which means the new terminal velocity must be higher.

The correct answer is C. Terminal velocity increases.
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*These A.I. responses have been individually checked to ensure they match the accepted answer, but explanations may still be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
Grade Gorilla uses Gemini, Deepseek and a range of other A.I. chatbots to generate the saved responses. Some answers have had human intervention for clarity or where the A.I. has not been able to answer the question.