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2nd Equation of Motion - Final Position

In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of ... more

3rd Equation of Motion - Final Position : acceleration independent

In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of ... more

1st Equation of Motion for Rotation - Angular Velocity

In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of ... more

2nd Equation of Motion for Rotation - Final Angle

In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of ... more

4th Equation of Motion for Rotation - Angular Velocity : time independent

In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of ... more

3rd Equation of Motion for Rotation - Final Angle : acceleration independent

In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of ... more

1st Equation of Motion - Linear Velocity

In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of ... more

Coefficient of restitution ( two objects)

The coefficient of restitution (COR) of two colliding objects is typically a positive real number between 0.0 and 1.0 ... more

Uniform gravitational field without air resistance (altitude)

Free fall is any motion of a body where its weight is the only force acting upon it. If gravity is the only influence acting, then the acceleration is ... more

Displacement (Distance)

A displacement is the shortest distance from the initial to the final position of a point. For motion over a given interval of time, the displacement ... more

Freefall in Uniform Gravitational Field with Air Resistance (altitude)

In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In a Freefall in Uniform Gravitational Field with ... more

Perfectly inelastic collision

A collision is an isolated event in which two or more moving bodies (colliding bodies) exert forces on each other for a relatively short time. Collision is ... more

Elastic collision (final velocity of one of the two bodies in elastic collision)

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total ... more

Elastic collision (final velocity of the second of the two bodies in elastic collision)

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total ... more

Trajectory Range

A trajectory or flight path is the path that a moving object follows through space as a function of time. A trajectory can be described mathematically ... more

Acceleration

Acceleration, in physics, is the rate at which the velocity of an object changes over time. Mathematically, instantaneous acceleration—acceleration over an ... more

Acceleration of a simple harmonic motion

A simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement. The motion is sinusoidal in ... more

Uniform gravitational field without air resistance (velocity)

Free fall is any motion of a body where its weight is the only force acting upon it. Falling in air, as long as the force of gravity on the object is much ... more

Vertical Curve - Parabolic formula

Vertical Curves are the second of the two important transition elements in geometric design for highways, the first being Horizontal Curves. A vertical ... more

Mean angular motion - function of gravitational parameter

In orbital mechanics, mean motion (represented by n) is the angular speed required for a body to complete one orbit, assuming constant speed in a circular ... more

Ideal rocket equation (Tsiolkovsky rocket equation)

The Tsiolkovsky rocket equation, or ideal rocket equation describes the motion of vehicles that follow the basic principle of a rocket: a ... more

Trajectory Height

A trajectory or flight path is the path that a moving object follows through space as a function of time. A trajectory can be described mathematically ... more

Proper motion (right ascension)

Proper motion is the astronomical measure of the observed changes in the apparent places of stars or other celestial objects in the sky, as seen from the ... more

Mean angular motion

In orbital mechanics, mean motion (represented by n) is the angular speed required for a body to complete one orbit, assuming constant speed in a circular ... more

Distance Law of Sound Pressure

Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average, or equilibrium) atmospheric pressure, caused by a sound ... more

Worksheet 289

Prior to manned space flights, rocket sleds were used to test aircraft, missile equipment, and physiological effects on human subjects at high speeds. They consisted of a platform that was mounted on one or two rails and propelled by several rockets. Calculate the magnitude of force exerted by each rocket, called its thrust T , for the four-rocket propulsion system shown in the Figure below. The sled’s initial acceleration is 49 m/s 2, the mass of the system is 2100 kg, and the force of friction opposing the motion is known to be 650 N.

A sled experiences a rocket thrust that accelerates it to the right.Each rocket creates an identical thrust T . As in other situations where there is only horizontal acceleration, the vertical forces cancel. The ground exerts an upward force N on the system that is equal in magnitude and opposite in direction to its weight,w.The system here is the sled, its rockets, and rider, so none of the forces between these objects are considered. The arrow representing friction ( f ) is drawn larger than scale.
Assumptions: The mass of the Sled remains steady throughout the operation

Strategy

Although there are forces acting vertically and horizontally, we assume the vertical forces cancel since there is no vertical acceleration. This leaves us with only horizontal forces and a simpler one-dimensional problem. Directions are indicated with plus or minus signs, with right taken as the positive direction. See the free-body diagram in the figure.

Solution

Since acceleration, mass, and the force of friction are given, we start with Newton’s second law and look for ways to find the thrust of the engines. Since we have defined the direction of the force and acceleration as acting “to the right,” we need to consider only the magnitudes of these quantities in the calculations. Hence we begin with

Force (Newton's second law)

Fnet is the net force along the horizontal direction, m is the rocket’s mass and a the acceleration.

We can see from the Figure at the top, that the engine thrusts add, while friction opposes the thrust.

Subtraction

Tt is the total thrust from the 4 rockets, Fnet the net force along the horizontal direction and Ff the force of friction.

Finally, since there are 4 rockets, we calculate the thrust that each one provides:

Division

T is the individual Thrust of each engine, b is the number of rocket engines

Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/

Relativistic kinetic energy of rigid bodies

In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a ... more

Velocity of a simple harmonic motion

A simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement. The motion is sinusoidal in ... more

Angle of elevation (for object following a ballistic trajectory)

A trajectory or flight path is the path that a moving object follows through space as a function of time. A trajectory can be described mathematically ... more

Impulse (Velocity)

Impulse is the product of a force and the time, for which it acts. The impulse of a force acting for a given time interval is equal to the change in linear ... more

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