Equation of Motion of a Particle acted on by a retarding force

Thread starter physconomics
Start date Jan 16, 2020
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Equation of motion Force Motion Particle

In summary, the equation of motion of a particle acted on by a retarding force is a mathematical representation that describes the motion of a particle under the influence of a force that opposes its direction of motion. It is derived using Newton's second law of motion and can be used to predict the future motion of the particle by considering its initial conditions. A retarding force is a force that acts in the opposite direction of an object's motion, slowing it down, and ultimately causing it to come to a stop. Its magnitude depends on various factors and affects the particle's velocity and acceleration, with a greater force resulting in a faster deceleration.

Jan 16, 2020

physconomics

Homework Statement: The equation of motion is $$\frac{d^2r}{dt^2} = a - y\frac{dr}{dt}$$
At time t = 0, $$r = r_0$$ and $$\frac{dr}{dt} = v_0$$
Show that $$d[a \times (yr + dr/dt]/dt = 0$$
and find the differential equation satisifed by $$s = a.r$$

Relevant Equations: Unsure

I really can't figure out where to even start on this question

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Jan 17, 2020

DEvens

Education Advisor

Gold Member

Can you fix the brackets in the expression you are to show is 0? Also, is "a" a constant? And is y a function of t?

Related to Equation of Motion of a Particle acted on by a retarding force

1. What is the equation of motion for a particle acted on by a retarding force?

The equation of motion for a particle acted on by a retarding force is given by Newton's second law of motion, which states that the net force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a). In this case, the retarding force (FR) is subtracted from the applied force (F) in the equation, resulting in the following equation: F - FR = ma.

2. How do you calculate the magnitude of the retarding force?

The magnitude of the retarding force can be calculated using the equation F = ma, where F is the net force acting on the object, m is the mass of the object, and a is the acceleration. In this case, the acceleration is the negative value of the object's velocity, as the retarding force is acting in the opposite direction of the motion.

3. What factors affect the magnitude of the retarding force?

The magnitude of the retarding force can be affected by several factors, including the mass of the object, the velocity of the object, and the nature of the retarding force (such as friction or air resistance). Additionally, any external forces acting on the object can also affect the magnitude of the retarding force.

4. How does the retarding force affect the motion of the particle?

The retarding force acts in the opposite direction of the object's motion, causing it to slow down or eventually come to a stop. The magnitude of the retarding force determines how quickly the object will decelerate. If the retarding force is greater than the applied force, the object will experience a net force in the opposite direction, resulting in negative acceleration or deceleration.

5. Can the retarding force ever be greater than the applied force?

Yes, the retarding force can be greater than the applied force, resulting in negative acceleration or deceleration. This can occur when there is a strong opposing force acting on the object, such as air resistance or friction. In some cases, the retarding force may also be equal to the applied force, resulting in a net force of zero and no change in the object's motion.