Physics: Resultant and Equilibrium of Forces

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

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 $Nm^2/kg^2$.

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.

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

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

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

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

<p>θ = 6.31°.</p> Signup and view all the answers

<p>The body is in equilibrium.</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

<p>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.</p> Signup and view all the answers

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

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

<p>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.</p> Signup and view all the answers

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

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

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

<p>AB = F1 and BE = F2 cos θ.</p> Signup and view all the answers

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

<p>When θ = 90°.</p> Signup and view all the answers

<p>R = F1 + 2F1F2 + F2^2.</p> Signup and view all the answers

<p>sin² θ + cos² θ = 1.</p> Signup and view all the answers

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

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

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

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

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

The process of combining multiple forces into a single resultant force.

The process of breaking a force into its components, usually along the x and y axes.

The rotational effect produced by a force about a point, calculated as force multiplied by the distance to the point.

States that the moment of a force about a point is equal to the sum of the moments of its components about that point.

A system of two equal and opposite forces whose effect is to produce rotation without translation.

The single force that represents the combined effect of multiple forces acting at different points.

If two forces acting on a body are represented by the triangle's sides, the resultant is the closing side.

Forces that act on the same point, potentially creating a resultant force.

Two specific forces used in examples of resultant and triangle law derivations.

States that if two forces acting on a body are represented as adjacent sides of a parallelogram, their resultant is the diagonal across.

Using the triangle law to combine two forces at a time for a resultant.

In the context, R1 represents the resultant of forces F1 and F2.

Visual representations showing the relationship and direction of forces acting on an object.

The combined effect of two forces, F1 and F2, calculated as R = F1 + F2.

R is calculated using R = F1 + 2F1F2 cos θ + F2².

F2 can be broken into horizontal (BE) and vertical (CE) components.

The angle α is determined by the tangent of the ratio of vertical to horizontal forces.

When θ is 90°, R equals the sum of F1 and F2.

When θ is 0°, R simplifies to F1 + F2.

The identity sin²θ + cos²θ = 1 is fundamental in mechanics.

F2 can be expressed as BE = F2 cos θ and CE = F2 sin θ.

The total of all forces acting vertically must equal zero for vertical equilibrium.

The angle contributing to force components in different directions (θ in this case).

sin A + sin B = 2 sin( (A+B)/2 ) cos( (A-B)/2 ) used to simplify calculations with angles.

The rate of change of velocity of an object moving along a circular path.

The angle at which a road is inclined to help vehicles negotiate curves safely.

The speed for which a road or railway curve is designed for optimal safety.

Loss of traction leading to sliding out of control on a banked surface.

Movement of an object in a circular path characterized by rotation around an axis.

Constant rate of rotation where an object spins at the same speed throughout.

The study of forces and torques that cause rotation in solid objects.

Energy possessed by an object due to its rotation, calculated based on mass and rotation speed.

A fundamental physical constant that quantifies the strength of gravity in the equation F = G(m1m2/d²).

The measurement unit of the gravitational constant G is Nm²/kg², showing the relationship of force, mass, and distance.

The gravitational force between two masses is calculated using F = G(m1m2/d²).

The weight of a body on Earth, denoted as W, is the gravitational force acting on it by Earth.

The weight of 1 kg mass on Earth's surface is approximately 9.81 N due to gravitational attraction.