Question

the kinetic energy of a moving object changes from ( k_0 ) to ( 4k_0 ). by what factor does the magnitude of the objects momentum change?
a 1
b 2
c 4
d 16

Explanation:

Step1: Recall formulas for KE and momentum

Kinetic energy \( K = \frac{p^2}{2m} \), where \( p \) is momentum, \( m \) is mass.
Initial: \( K_0 = \frac{p_0^2}{2m} \)
Final: \( 4K_0 = \frac{p_f^2}{2m} \)

Step2: Divide final KE by initial KE

\( \frac{4K_0}{K_0} = \frac{\frac{p_f^2}{2m}}{\frac{p_0^2}{2m}} \)
Simplify: \( 4 = \frac{p_f^2}{p_0^2} \)

Step3: Solve for \( \frac{p_f}{p_0} \)

Take square root: \( \frac{p_f}{p_0} = \sqrt{4} = 2 \)

Answer:

B. 2