Question 1:

1. Correct Placement for the Force of Gravity

The force of gravity acts on the center of mass of an object and is always directed towards the center of the larger celestial body. For the meteor, the force of gravity is a pull towards the center of the Earth, downwards.

(Edited - the Silverback)

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Question 2:

Incorrect Label for the Force of Gravity

The force of gravity on an object is commonly called weight. The mathematical expression for weight is mg, where m is the mass of the object and g is the acceleration due to gravity. When an object is falling, the force is often described as the downwards force of gravity from the Earth.

However, the term "gravity" is not a force in itself. It is the fundamental interaction or phenomenon that causes the force. The force itself is the gravitational force or, more commonly, weight. Therefore, using "gravity" as a label for the force is a common mistake and is often considered incorrect in physics.

*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:

Let's break down the components of this diagram:

The Meteor: Represent it as a small circle or dot (O) to signify it's a point.

Force of Gravity (Weight):

Direction: Draw an arrow pointing directly downwards from the meteor. This arrow should point towards the center of the Earth.

Label: Label this arrow "Force of Gravity," "Weight," or "mg."

Size: The length of this arrow represents the magnitude of the gravitational force.

Air Resistance (Drag Force):

Direction: Draw an arrow pointing directly upwards from the meteor, opposing the direction of motion.

Label: Label this arrow "Air Resistance" or "Drag Force."

Size: This is the crucial part for showing the meteor is slowing down. Since the meteor is decelerating (slowing down), the upward force of air resistance must be larger than the downward force of gravity. Therefore, draw this arrow significantly longer than the gravity arrow.

Key things this diagram conveys:

Net Force: Because the upward air resistance arrow is longer than the downward gravity arrow, the net force on the meteor is upwards.

Deceleration: An upward net force on an object moving downwards means it is decelerating, or slowing down, which matches the problem description.

Point Object: The forces are drawn originating from or acting upon the "point" of the meteor.

Here's an illustrative diagram:

^
|
| Air Resistance (F_air) - LONGER arrow
|
|
O <-- Meteor (point)
|
| Force of Gravity (mg / Weight) - SHORTER arrow
v

This corresponds to diagram 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.
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:

The correct diagram showing all the forces acting on a stationary block on a slope is B.

Analysis of the Forces
There are three main forces acting on the block:

Weight (W or F_g): This force is due to gravity and always acts vertically downwards, from the center of mass of the object towards the center of the Earth. It does not act perpendicular to the slope, unless the slope is horizontal.

Normal Force : This is the force the surface exerts on the object to support it. It acts perpendicular to the surface of the slope. This force is a reaction to the component of the object's weight that pushes it into the slope.

Friction: Since the block is stationary on the slope, there is a static frictional force preventing it from sliding down. This force acts parallel to the surface of the slope and points upwards, opposing the component of gravity that is pulling the block downwards along the slope.

Why Diagram B is Correct
Diagram A is incorrect because the normal force is not perpendicular to the slope.

Diagram B correctly shows all three forces: the weight (W) acting vertically downwards, the normal force (N) acting perpendicular to the slope, and the frictional force (F_f) acting up the slope. The arrows are placed correctly.

Diagram C is incorrect there is no normal contact force.

Diagram D is incorrect because it shows the normal force acting vertically upwards, which is only true for a flat, horizontal surface.

*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 5:

The correct answer is D. There is no resultant force.

Explanation

Since the block is stationary on the slope, it's in a state of equilibrium. This means all the forces acting on it are balanced. The resultant force, which is the vector sum of all the forces, must be zero.

The forces on the block are:

• Weight: Acts vertically downwards.

• Normal force: Acts perpendicular to the slope, upwards.

• Static Friction: Acts parallel to the slope, upwards.

The downward component of the weight is balanced by the upward force of static friction. The perpendicular component of the weight is balanced by the normal force. Because all forces are balanced, the net force is zero, so there is no resultant force acting on the block.

*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 B. Normal force = m.g.cosθ.

Explanation
The normal force is the force exerted by a surface to prevent an object from penetrating it. On a horizontal surface, the normal force is equal to the object's weight (mg). However, on an inclined plane, the normal force is equal to the component of the weight that is perpendicular to the slope.

To find this component, we resolve the weight vector (mg), which acts vertically downwards, into two components:

• One component acting perpendicular to the slope.
• One component acting parallel to the slope.

The component of weight perpendicular to the slope is the force pushing the block into the slope. Using trigonometry, this component is equal to mg×cosθ.

Since the block is stationary and not moving perpendicular to the slope, the normal force (N) must be equal and opposite to this component of the weight.

Therefore, the normal force is given by the equation:
N=mgcosθ

*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 7:

Calculation
To find the force of air resistance, we need to consider the net force acting on the stone. The net force is the sum of the downward force of gravity and the upward force of air resistance.

Calculate the force of gravity (F_g)

F_g=mass × acceleration due to gravity (g)
Assuming g≈9.8 m/s²
F_g=0.5 kg×9.8 m/s² =4.9 N

Calculate the net force (F_net):
The net force is what causes the stone to accelerate.
F_net =mass×acceleration =0.5 kg×3 m/s
=1.5 N

Find the force of air resistance (F_air):
The forces are in opposite directions, so the net force is the difference between the force of gravity (downwards) and the force of air resistance (upwards).
F_net =F_g - F_air
​
1.5 N=4.9 N−F_air
​

So F_air =4.9 N−1.5 N

F_air = 3.4 N

This value is approximately 3.5 N, which corresponds to answer 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 8:

To find the force, we use Hooke's Law, which states that the force applied to a spring is directly proportional to its extension. The formula for Hooke's Law is:
F=kx
Where:

F is the force applied (in Newtons, N)

k is the spring constant (in N/m)

x is the extension (in meters, m)

Calculation
First, we need to convert the extension from centimeters to meters.
5 cm=0.05 m

Now, we can plug the values into the formula:
F=(500 N/m)×(0.05 m)
F=25 N

*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:

Calculation

To find the extension, you need to use a variation of Hooke's Law ( F = kx), where the force ( F) on the spring is the weight of the added mass.

1. Calculate the force (weight): F = mass × acceleration due to gravity (g) We use g ≈ 10 N/kg for simplicity in these types of problems. F = 4 kg × 10 N/kg = 40 N

2. Rearrange Hooke's Law to solve for extension ( x): x = F/k​

3. Substitute the values and solve for x: x = 40 / 500 = 0.08 m

4. Convert the extension to centimeters: x = 0.08 m × 100 cm/m = 8 cm

   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.
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Question 10:

The correct answer is D. k = 250 N m⁻¹ and L = 27 cm.

Finding the Spring Constant (k)
Hooke's Law states that the force applied to a spring is proportional to its extension (F=kx). The force here is the weight of the mass (F=mg). The extension (x) is the difference between the stretched length and the natural length (x=stretched length−natural length).

Let L₀ be the natural length of the spring.
We have two scenarios:

Scenario 1: A mass of 2 kg gives a length of 15 cm.
F₁=m g=2 kg×10 N/kg =20 N
x₁ =15 cm−L₀
​
Using Hooke's Law: 20=k(15−L₀) (Equation 1)

Scenario 2: A mass of 3 kg gives a length of 19 cm.
F₂ =m g=3 kg×10 N/kg =30 N
x₂=19 cm−L₀

Using Hooke's Law: 30=k(19−L₀) (Equation 2)

We now have a system of two equations with two unknowns (k and L₀)
Let's divide Equation 2 by Equation 1 to eliminate k:
30/20 = [ k(19−L₀) ] / [k(15−L₀) ]
​
1.5= (19-L₀) / (15 -L₀)

1.5(15−L₀)=19−L₀
​
22.5−1.5L₀=19−L₀
​
3.5=0.5L₀

L₀ =7 cm

Now, substitute L₀ back into Equation 1 to find k:
20=k(15−7)
20=k(8)
k= 20/8 ​
=2.5 N/cm

To convert the spring constant to N/m, we multiply by 100 (since there are 100 cm in a meter).
k=2.5 N/cm×100=250 N/m

Finding the Length for a 5 kg Mass
Now that we know k=250 N/m and the natural length L₀ =7 cm, we can find the length when a 5 kg mass is added.

Calculate the force:
F =m g=5 kg×10 N/kg =50 N

Calculate the extension (x):
x= F/k
​ x= 50 / 250  ​
x =0.2 m

Convert the extension to cm:
x=0.2 m×100=20 cm

Find the final length (L):
L=L₀+x
L=7 cm+20 cm=27 cm

The correct answer is D. k = 250 N m⁻¹ and L = 27 cm.

*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.