How to calculate the 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. it is unit of measurement is Newtons (N) and the dimensional formula is given by [M¹L¹T^-2]. Its formula equals the product of 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 traveled 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.

Derivation

Consider an object of mass m which 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 force 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

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

Solution:

m = 2

v = 4

t = 2

Using the formula we get,

F = mv/2t

= 2 (4) / 2 (2)

= 8/4

= 2 N

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

Solution:

m = 3

v = 8

t = 3

Using the formula we get,

F = mv/2t

= 3 (8) / 2 (3)

= 24/6

= 4 N

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:

F = 10

v = 5

t = 4

Using the formula we get,

F = mv/2t

=> m = 2Ft/v

= 2 (10) (4) / 5

= 16 kg

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

Solution:

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

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:

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

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

Solution:

E = 20

d = 2

Using the formula we get,

F = E/d

= 20/2

= 10 N

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

Solution:

F = 40

d = 4

Using the formula we get,

F = E/d

=> E = Fd

= 40 (4)

= 160 J

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