Physics: Resultant and Equilibrium of Forces

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Questions and Answers

What is the formula for the force of gravity between two objects with masses m1 and m2, separated by a distance d? Express your answer in terms of the gravitational constant G.

The formula for the force of gravity is: $F = G \frac{m_1 m_2}{d^2}$

Explain the concept of the gravitational constant G and describe its units. What is its approximate value?

The gravitational constant G is a fundamental constant that determines the strength of gravitational force. Its units are $Nm^2/kg^2$. The approximate value of G is 6.673 x 10^-11 $Nm^2/kg^2$.

Calculate the force of gravity between a 10 kg object and a 5 kg object separated by a distance of 1 meter. Show your work.

Using the formula F = G(m1m2/d^2), we have: F = (6.673 x 10^-11 Nm^2/kg^2) * (10 kg * 5 kg) / (1 m)^2 = 3.3365 x 10^-9 N.

How is the weight of an object related to the force of gravity? Explain using the example of a 1 kg object on Earth's surface.

The weight of an object is the force of gravity exerted on it by the Earth. In the case of a 1 kg object on Earth's surface, the force of gravity is calculated to be approximately 9.81 N, which is also its weight. Signup and view all the answers

Why is the gravitational force between two objects near Earth's surface negligible compared to the force between the Earth and those objects?

The force of gravity between two objects near Earth's surface is negligible because the masses of those objects are significantly smaller than the Earth's mass. As the force of gravity is proportional to the product of the masses, the difference in mass results in a much weaker force between the two objects. Signup and view all the answers

What condition must be met for the resultant of the three forces to be directed parallel to the plane in the context provided?

The component of reaction in the y-direction must be zero, meaning ΣFy = 0. Signup and view all the answers

In the equation ΣFy = 0, what force contributions must be considered according to the solution?

The contributions are from 300N sin θ, 300N sin(40° + θ), and the 500N sin 30°. Signup and view all the answers

What mathematical relationship was used to simplify the equation involving sin θ and sin(40° + θ)?

The identity used was sin A + sin B = 2 sin( (A+B)/2 ) cos( (A-B)/2 ). Signup and view all the answers

Calculate the angle θ that satisfies the equilibrium condition of the system of forces described.

θ = 6.31°. Signup and view all the answers

What state is a body in when all forces acting on it are balanced as indicated in the text?

The body is in equilibrium. Signup and view all the answers

What does line AB represent in the context of the triangle law of forces?

Line AB represents the force F1 in the triangle law of forces. Signup and view all the answers

According to the triangle law of forces, how is the resultant represented?

The resultant is represented by the closing side of the triangle taken from the first point to the last point. Signup and view all the answers

What is the significance of constructing triangle ABD in the context of forces?

Constructing triangle ABD allows us to visually determine the resultant force AD from the individual forces F1 and F2. Signup and view all the answers

How can multiple concurrent forces be analyzed using the triangle law?

Multiple concurrent forces can be combined two at a time using the triangle law until the resultant of all forces is obtained. Signup and view all the answers

What is the first step in applying the triangle law of forces?

The first step is to represent the forces as sides of a triangle, placing them one after another. Signup and view all the answers

In Fig. 1.9, what does line AC represent?

Line AC represents the resultant R1 of the two forces F1 and F2. Signup and view all the answers

What geometric shape is crucial for determining the resultant of two forces using the triangle law?

A triangle is crucial for determining the resultant of two forces using the triangle law. Signup and view all the answers

If two forces are represented by the sides of a triangle, what does this imply about their interaction?

It implies that the two forces can be combined to find a single resultant force acting on the body. Signup and view all the answers

What is the difference between concurrent and non-concurrent forces?

Concurrent forces are forces that act on a single point simultaneously, while non-concurrent forces act on different points in space. Signup and view all the answers

Explain Varignon’s Theorem in the context of moment of a force.

Varignon’s Theorem states that the moment of a force about a point is equal to the algebraic sum of the moments of its components about that same point. Signup and view all the answers

Define equilibrium in the context of connected bodies.

Equilibrium of connected bodies occurs when the sum of forces and the sum of moments acting on the system are both zero. Signup and view all the answers

What is meant by the resolution of forces?

The resolution of forces is the process of breaking down a single force into two or more component forces that act along specified directions. Signup and view all the answers

How does one determine the resultant of a system of non-concurrent forces?

The resultant of a system of non-concurrent forces can be determined by vector addition of all individual force vectors considering their magnitudes and angles. Signup and view all the answers

What is a couple in mechanics?

A couple is a pair of equal and opposite forces whose lines of action do not coincide, creating a rotational effect. Signup and view all the answers

Describe the general method for composing forces.

The general method for composing forces involves the vector addition of forces acting at various angles to find a single resultant force that produces the same effect. Signup and view all the answers

What are x and y intercepts of a resultant force?

The x and y intercepts of a resultant force are the points where the resultant vector crosses the x-axis and y-axis, respectively, indicating its directional influence in a coordinate system. Signup and view all the answers

What is the formula for the resultant R of the forces F1 and F2?

R = F1 + 2F1F2 cos θ + F2^2. Signup and view all the answers

Explain how the values of AB and BE are determined in relation to forces F1 and F2.

AB = F1 and BE = F2 cos θ. Signup and view all the answers

What does the equation tan α = CE / AE represent in this context?

It represents the inclination of the resultant force to the direction of F1. Signup and view all the answers

At what angle θ does the resultant R equal F1 + F2?

When θ = 90°. Signup and view all the answers

What happens to the resultant R when θ = 0°?

R = F1 + 2F1F2 + F2^2. Signup and view all the answers

Define the relationship between sin² θ and cos² θ in the context of the resultant force.

sin² θ + cos² θ = 1. Signup and view all the answers

How is the resistance of each force to the resultant evaluated?

Through the components AB and BE derived from forces F1 and F2. Signup and view all the answers

What do the variables F1 and F2 represent in this analysis?

F1 and F2 represent the magnitudes of two forces acting at an angle θ to each other. Signup and view all the answers

Explain the concept of 'super elevation' in the context of railway tracks, and why it is necessary.

Super elevation refers to the banking of railway tracks, where the outer rail is raised higher than the inner rail. This is essential to counteract the centrifugal force experienced by a train moving on a curved track. Without super elevation, the train would tend to tilt outward, potentially causing derailment. Signup and view all the answers

Describe the relationship between angular velocity and linear velocity in the context of a rotating rigid body. Provide an equation illustrating this relationship.

Angular velocity (ω) represents the rate of change of angular displacement, while linear velocity (v) refers to the speed of a point on the rotating object. The relationship is given by: v = ω * r, where r is the distance of the point from the axis of rotation. Signup and view all the answers

Explain the concept of 'designed speed' for a banked road. What factors influence this designed speed?

Designed speed refers to the optimal speed at which a vehicle should travel on a banked road to maintain stability and prevent skidding. The designed speed is influenced by factors like the angle of banking, the radius of curvature of the road, and the coefficient of friction between the tires and the road. Signup and view all the answers

What is the significance of the kinetic energy of a rotating body? How is it calculated?

The kinetic energy of a rotating body represents the energy possessed due to its rotational motion. It is significant because it plays a crucial role in understanding the total energy of the rotating body and its ability to do work. The kinetic energy (KE) of a rotating body is calculated using the formula KE = (1/2) * I * ω² where I is the moment of inertia and ω is the angular velocity. Signup and view all the answers

What are the two main ways a vehicle can skid on a banked road? Explain the factors contributing to each type of skidding.

A vehicle can skid on a banked road due to either oversteering or understeering. Oversteering occurs when the vehicle's rear tires lose traction and slip, potentially causing the vehicle to spin out. This is often caused by excessive speed or sharp steering. Understeering, on the other hand, occurs when the front tires lose traction and the vehicle slides straight ahead without turning. This can be due to factors like insufficient speed or slippery road conditions. Signup and view all the answers

Explain why banking roads is necessary to prevent vehicles from skidding during turns.

Banking roads helps counteract the centrifugal force that acts on a vehicle moving along a curved path. Without banking, the centrifugal force would push the vehicle outward, potentially causing it to skid. By tilting the road inward, a component of the normal force opposes the centrifugal force, helping maintain the vehicle's stability. Signup and view all the answers

Outline the key factors that dictate the acceleration of a rigid body undergoing circular motion.

The acceleration of a rigid body in circular motion is determined by its tangential speed (v) and the radius of the circular path (r). The acceleration is directed towards the center of the circle and is given by the formula a = v²/r. Furthermore, any changes in the body's tangential speed will also contribute to the acceleration. Signup and view all the answers

Flashcards

Resultant Force

The single force which represents the combined effect of all other forces acting on a body.

Equilibrium

A state where the sum of forces and moments acting on a body is zero.