# How to Find Net Force with Mass and Velocity: Various Methods, Problems and Facts

The article discusses about the various methods on how to find net force with mass and velocity and its solved problems.

The net force, the sum of all forces, accelerates any object having mass by varying its velocity. The concepts encourage us to take distinct approaches on how to find net force with mass and velocity by employing Newton’s law of motion, various force formulas and the Work-Energy theorem.

In the previous article, we have examined various net force examples. Each force acting on an object sets its acceleration. Hence, we simply add all different types of forces acting on an object to estimate one net force that accelerates an object in one direction by changing its motion.

## How to Find Net Force with Mass and Velocity by Momentum Change?

Newton’s second law of motion assists us in determining the net force in terms of mass and velocity.

Newton’s second law says an object’s momentum P varies when a net force is employed. The momentum change means an object having mass m at rest or in motion changes its velocity v per unit time t when it moves from one position to another.

As per Newton’s second law,

But Momentum P = mv,

Fnet =(mv-mv0)/(t-t0)

Since mass m does not change when net force acts,

Fnet =m*[(v-v0)/(t-t0)]

An object’s velocity change (v=v0) per unit time change (t-t0) is an object’s acceleration ‘a’ due to net force.

a=(v-v0)/(t-t0)=Δv/Δt

Hence, Fnet = ma …………………. (*)

## The airplane of mass 40kg moves 20km/hr along the ground in 10 min. If life force applies on the same airplane, it takes off with a 30km/hr velocity in 15 minutes. What is the net force acting on the airplane?

Given:

m = 40kg

v = 30km/hr

v0 = 20km/hr

t = 15min

t0 = 10min

To Find: Fnet =?

Formula:

Fnet ==m*[(v-v0)/(t-t0)]

And

Fnet = F1+F2+…FN

Solution:

The net force on the airplane is calculated using Newton’s second law of motion.

Fnet =m*[(v-v0)/(t-t0)

Substituting all values,

Fnet =40*[(30-20)/(15010)]

Fnet = 80

The net force on an airplane with a mass of 40kg flying with a 30km/hr velocity is 80N.

## How to Find Net Force with Mass and Velocity using Force Formulas?

The net force with mass and velocity is estimated by formulas of different types of forces.

When we apply a force on an object along the ground, the gravity force which always acts on an object is balanced by the normal force. The ground surface also exerts the friction force opposite the applied force. Both equal and opposite forces help us to estimate the net force with mass and velocity.

The normal force (mg) and gravity (mg) cancel each other. That means, FN + (-Fg) = mg – mg = o

The applied force formula is,

Fi = ma

The friction force formula is,

Ffric = μFN = μmg

The net force formula is given by,

Fnet = Fi + (-Ffric)

Fnet = ma – μmg

Fnet = m (a – μg)

The net force formula with mass and velocity using force formulas is given by,

Fnet =m*[(v-v0)/(t-t0)]-μg

## The sled has a mass of 5kg sliding on the ice surface with a 20km/hr in 5 min. Since the ice surface has a coefficient of friction of about 1, it exerts the sliding friction force, reducing the sled’s velocity to 15km/hr in 2 min. Calculate the net force acting on the sled. (Given: g= 9.8m/s2)

Given:

m = 5kg

v = 15km/hr

v0 = 20km/hr

t = 10min

t0 = 5min

μ = 1

g= 9.8m/s2

To Find: Fnet =?

Formula:

Fnet =m*[(v-v0)/(t-t0)]-μg

Solution:

The net force on the sled is calculated as,

Fnet =m*[(v-v0)/(t-t0)]-μg

Substituting all values,

Fnet = 54

The net force on the sled has a mass of 5kg, and a velocity of 15km/hr is 54N.

## How to find Net Force with Mass and Velocity and Distance?

The net force with mass, velocity, and distance is estimated t by the work-energy theorem.

An object having mass at rest is said to work done when it moves with a certain velocity from one position to another. The acceleration is caused when a net force acts on it, transforming its stationary potential energy into kinetic energy to perform work.

The work done formula is,

W = Fnetd

The work done is the change in an object’s kinetic energy. i.e., 1/2m(v-v0)

Therefore, the net force with mass, velocity and distance using the work-energy formula is given by,

1/2m(v-v0)=Fnetd

Fnet=[m(v-v0)]\2d

## ●      Calculate the net force acting on the car with mass, velocity and distance.

Given:

m = 50kg

v = 40km/hr

v0 = 30km/hr

t = 20min

t0 =15min

To Find:

1. d=?
2. Fnet=?

Formula:

1)Kinematics equation of motion

d=(v+v0)/2

2)Fnet=[m(v-v0)]\2d

Solution:

The distance travelled by car is calculated using the second Kinematics equation of motion.

d = [(v+v0)/2]t

Substituting all values,

d=[(30+40)/2]*20

d=35*20

d= 70

The distance travelled by a car when net force acts is 70m.

Using the Work-Energy formula, let’s calculate the net force on a car with mass, velocity and distance.

Fnet=[m(v-v0)]\2d

Substituting all values,

Fnet=[50(40-30)]/(2*70)

Fnet=500\140

Fnet = 3.57

The net force acting on the car is 3.57N.