A force of 20 n acts on a body of mass 4 kg for 5 s initially at rest. calculate the velocity accuried by the body and change in momentum of the body.
Answers
Concept:
If other information is available, a set of four equations known as the kinematic equations can be used to forecast unknown information about an object's motion. The first kinematical equation is given as, v = u + at
Given:
Force, F = 20 N
Mass, m = 4 kg
Time period, t = 5s
Initial velocity, u = 0m/s
Find:
We need to determine the velocity, v acquired by the body and the change in momentum of the body, P.
Solution:
Force can be defined as an effect that can alter an object's motion. According to Newton's second law, it can be mathematically expressed as F = ma where F = force, m = mass of an object and a = acceleration
To apply the 1st kinematic equation we need to determine the acceleration due to gravity therefore Newton's 2nd law becomes,
a = F/m = 20/4 = 5m/s²
According to the first kinematic equation, v = u + at
Since the body is initially at rest, initial velocity, u = 0m/s.
Therefore, the first kinematic equation becomes, v = 0 + 5×5 = 25 m/s
hence, the velocity acquired by the body is 25 m/s.
The relationship between a particle's mass and velocity can be used to define momentum. Being a vector quantity, momentum possesses both magnitude and direction.
Momentum, P = mv
P = 4×25 = 100 kgm/s
Hence, the change in momentum of the body is 100 kgm/s
Thus, the velocity acquired by the body and change in momentum of the body is 25 m/s and 100 kgm/s, respectively.
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