Concept:
Momentum of a body is equal to the product of its mass and its velocity. It is a vector quantity; i.e., it has both magnitude and direction.
Momentum = mass × velocity.
Kinetic energy (K.E):
The energy possessed by a body by the virtue of its motion is called kinetic energy.
The expression for kinetic energy is given by:
\(KE = \frac{1}{2}m{v^2}\)
Where m = mass of the body and v = velocity of the body
Calculation:
Given:
Force applied on both body F = 20 N,
Mass of first body m1 = 2 kg, Mass of second body m2 = 2.5 kg
Time duration in which force acted is t = 2s,
Momentum and Acceleration of first body m1 = 2 kg,
As we know that acceleration can be found as
⇒ \(a_1=\frac{F}{m_1}\) (∵ F = m1a1)
⇒ \(a_1=\frac{20}{2}=10\) m/s2
Given that the body is initially at rest means the initial velocity u1 of the first body is zero and we have to find the final velocity v1, hence after getting the final velocity we can easily find the Kinetic energy and momentum.
∴ \(a_1=\frac{v_1-u_1}{t}\)
∴ v1 = a1⋅t + u1 = (10)(2) + 0 = 20 m/sec
Now from the final velocity of first body we can find the ratio of Momentum P1 and Kinetic energy KE1 of the body as below
⇒ Momentum of First body P1 = m1v1
∴ P1 = 2 × 20 = 40 kg-m/sec
⇒ Kinetic energy of first body:
\(KE_1=\frac{1}{2}m_1v_1^2\)
\(KE_1=\frac{1}{2}\times 2\times (20)^2=400\) kg-m2/sec2 or J
Momentum and Acceleration of second body m2 = 2.5 kg,
As we know that acceleration can be found as
⇒ \(a_2=\frac{F}{m_2}\) (∵ F = m2a2)
⇒ \(a_2=\frac{20}{2.5}=8\) m/s2
Given that the body is initially at rest means the initial velocity u2 of the first body is zero and we have to find the final velocity v2 , hence after getting the final velocity we can easily find the Kinetic energy and momentum.
∴ v2 = a2⋅t + u2 = (8)(2) + 0 = 16 m/sec
Now from the final velocity of first body we can find the ratio of Momentum P2 and Kinetic energy KE2 of the body as below.
⇒ Momentum of First body P2 = m2v2
∴ P2 = 2.5 × 16 = 40 kg-m/sec
⇒ Kinetic energy of second body:
\(KE_2=\frac{1}{2}m_1v_1^2\)
\(KE_2=\frac{1}{2}\times 2.5\times (16)^2=320\) kg-m2/sec2 or J
Ratio of Momentum:
\(\frac{p_1}{p_2}=\frac{40}{40}=1:1\)
Ratio of Kinetic Energy:
\(\frac{KE_1}{KE_2}=\frac{400}{320}=5:4\)