How to calculate the Impact Force?

Impact force is calculated by finding the ratio of change in momentum of the object(s) involved in collision with the time period of collision. The formula for calculating impact force is:

F = Δp/Δt, where Δp is the change in momentum and Δt is the time period.

What is Impact Force?

Impact force is defined as a situation when some work is done to move an object a specific distance. It can be interpreted as the force produced when two items collide. An object collision occurs when one object collides with another. The impact force has a huge impact on an object in a short period of time. It is denoted by the symbol F, where the unit of measurement is Newtons (N) and the dimensional formula is given by [M¹L¹T^-2]. Its formula equals the product of the mass and velocity of a body to the twice time taken. In other words, it is the ratio of kinetic energy possessed by a body to the distance travelled by it.

Impact Force Formula

F = mv/2t

where,

F is the impact force,

m is the mass of the body,

v is the velocity of the body,

t is the time taken.

Proof of the formula

Consider an object of mass m that moves with a velocity v when some work W is done on it. The force applied is F and it moves the object to a distance of d units for t seconds.

We know the work done equals the product of fthe orce applied and distance travelled.

W = Fd ⇢ (1)

Also, the work done equals the kinetic energy of the body.

W = K.E. = 1/2 mv² ⇢ (2)

From (1) and (2) we get,

Fd = 1/2 mv²

F = mv²/2d

Putting d = vt, we get,

F = mv²/2vt

F = mv/2t

This derives the formula for impact force acting on a body.

Sample Problems

Let’s consider a few problems to find out how to use this formula.

Problem 1: Calculate the impact force acting on an object of mass 2 kg, velocity 4 m/s for 2 seconds.

Solution:

The impact force acting on this object with a mass of 2 kg and moving at a velocity of 4 m/s for 2 seconds. Hence,

m = 2

v = 4

t = 2

Using the formula we get,

F = mv/2t

= 2 (4) / 2 (2)

= 8/4

= 2 N

Therefore, the impact force acting on the object is 2 Newtons.

Problem 2: Calculate the impact force acting on an object of mass 3 kg, velocity 8 m/s for 3 seconds.

Solution:

To calculate the impact force, the given values for this problem are:

m = 3

v = 8

t = 3

Using the formula we get,

F = mv/2t

= 3 (8) / 2 (3)

= 24/6

= 4 N

Therefore, the impact force acting on the object is 4 Newtons.

Problem 3: Calculate the mass of the body if the impact force acting on an object is 10 N, and velocity is 5 m/s for 4 seconds.

Solution:

In this problem, we need to calculate the mass of an object given the impact force, velocity, and time. The given values are:

F = 10

v = 5

t = 4

Using the formula we get,

F = mv/2t

=> m = 2Ft/v

= 2 (10) (4) / 5

= 16 kg

Hence, the mass of the object is 16 kg.

Problem 4: Calculate the velocity of the body if the impact force acting on an object is 14 N and the mass is 2 kg for 2 seconds.

Solution:

Here, we need to determine the velocity of an object given the impact force, mass, and time. We have,

F = 14

m = 2

t = 2

Using the formula we get,

F = mv/2t

=> v = 2Ft/m

= 2 (14) (2) / 2

= 28 m/s

Hence, the velocity of the object is 28 m/s.

Problem 5: Calculate the time taken by the body if the impact force acting on an object is 30 N, mass is 4 kg, and velocity is 15 m/s.

Solution:

To calculate the time taken by an object given the impact force, mass, and velocity values as:

F = 30

m = 4

v = 15

Using the formula we get,

F = mv/2t

=> t = mv/2F

= 4 (15) / 2 (30)

= 60/60

= 1 s

So, the time taken by the object is 1 second.

Problem 6: Calculate the impact force acting on an object of kinetic energy 20 J if the distance travelled is 2 m.

Solution:

The given values are:

Kinetic Energy (E) = 20 J

Distance Traveled (d) = 2 m

We know that to determine the impact force, we have a formula: F = E/d, where F is the impact force, E is Kinetic Energy, and d is the distance travelled.

Hence, using the formula we get,

F = E/d

= 20/2

= 10 N

That is, the impact force acting on the object is 10 Newtons.

Problem 7: Calculate the kinetic energy of a body if the impact force acting on an object is 40 N and the distance travelled is 4 m.

Solution:

The given values to calculate the kinetic energy of a body are:

Impact Force (F) = 40

Distance Traveled (d) = 4

Using the formula we get,

F = E/d

=> E = Fd

= 40 (4)

= 160 J

Therefore, the kinetic energy of the body is 160 Joules.