Two bodies m1 and m2 (m1 > m2) have the same kinetic energy. Then their momentum p1 and p2

Let's assume that the two bodies, m1 and m2, have the same kinetic energy.

Step 1: Recall the formula for kinetic energy: KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.

Step 2: Since the kinetic energy is the same for both bodies, we can write the equation as (1/2)m1v1^2 = (1/2)m2v2^2.

Step 3: Rearrange the equation to solve for v1^2: v1^2 = (m2/m1)v2^2.

Step 4: Take the square root of both sides to solve for v1: v1 = sqrt((m2/m1)v2^2).

Step 5: Now, let's consider the momentum of each body. The momentum, p, is given by the formula p = mv, where m is the mass and v is the velocity.

Step 6: The momentum of m1, denoted as p1, is equal to m1v1.

Step 7: Similarly, the momentum of m2, denoted as p2, is equal to m2v2.

Step 8: Substitute the value of v1 from step 4 into the equation for p1: p1 = m1 * sqrt((m2/m1)v2^2).

Step 9: Simplify the equation for p1: p1 = sqrt(m1m2)v2.

Step 10: Substitute the value of v2 from step 5 into the equation for p2: p2 = m2 * v2.

Step 11: Simplify the equation for p2: p2 = m2v2.

Conclusion: From steps 9 and 11, we can see that p1 = sqrt(m1m2)v2 and p2 = m2v2. Since m1 > m2, it follows that sqrt(m1m2) > m2. Therefore, p1 > p2.