Two objects, A and B, have the same kinetic energy. A has a speed that is 12.1 times greater than the speed of B. What is the ratio of the mass of B to the mass of A?
I'm not sure how to do this one given... KE_A = KE_B & V_A = 12.1V_B
How do I find the ratio of the mass??
Notice that the problem says that the velocity of object A is 12.1 times GREATER than B:
Va = Vb + 12.1Vb = 13.1Vb.
Ma = Mass of object A.
Va = Velocity of object A.
Mb = Mass of object B.
Vb = Velocity of object B.
KE = Mb*(Vb)^2/2 = Ma*(13.1Vb)^2/2,
Mb*(Vb)^2/2 = Ma^(13.1Vb)^2,
Multiply both sides by 2:
Mb*(Vb)^2 = Ma*(13.1Vb)^2,
Divide both sides by (Vb)^2:
Mb = Ma*(13.1)^2,
Divide both sides by Ma:
Mb / Ma = (13.10^2 = 171.6m/s.
To find the ratio of the mass of B to the mass of A, we need to use the formula for kinetic energy and solve for the mass ratio.
Let's start by using the formula for kinetic energy:
KE = (1/2) * m * v^2
Where KE is the kinetic energy, m is the mass, and v is the speed.
Given that the kinetic energy of object A (KE_A) is equal to the kinetic energy of object B (KE_B), we can write the equation as:
(1/2) * m_A * v_A^2 = (1/2) * m_B * v_B^2
Since we are trying to find the ratio of the mass of B to the mass of A, let's divide both sides of the equation by m_A:
(1/2) * v_A^2 = (1/2) * (m_B / m_A) * v_B^2
Simplifying further, we get:
v_A^2 = (m_B / m_A) * v_B^2
Now, we are given that the speed of A (v_A) is 12.1 times greater than the speed of B (v_B), so we can substitute that into the equation:
(12.1v_B)^2 = (m_B / m_A) * v_B^2
Expanding and simplifying:
146.41 * v_B^2 = (m_B / m_A) * v_B^2
We can cancel out the v_B^2 terms:
146.41 = m_B / m_A
So, the ratio of the mass of B to the mass of A is 146.41:1.
Therefore, the ratio of the mass of B to the mass of A is approximately 146.41:1.