Question

question 12 of 20
a force of 16 n to the west is applied to each object below. which object will undergo the greatest change in momentum?
a. a 20 kg object that is moving east at 5 m/s
b. a 15 kg object that is moving east at 5 m/s
c. a 20 kg object that is moving east at 10 m/s
d. a 15 kg object that is moving east at 10 m/s

Explanation:

Step1: Recall impulse - momentum theorem

Impulse \(J = F\Delta t=\Delta p\). Here, \(F = 16N\) is the same for all objects. The change in momentum \(\Delta p\) depends on the initial momentum \(p = mv\).

Step2: Calculate initial momentum for option A

\(p_A=m_Av_A=20\times5 = 100kg\cdot m/s\)

Step3: Calculate initial momentum for option B

\(p_B=m_Bv_B=15\times5 = 75kg\cdot m/s\)

Step4: Calculate initial momentum for option C

\(p_C=m_Cv_C=20\times10 = 200kg\cdot m/s\)

Step5: Calculate initial momentum for option D

\(p_D=m_Dv_D=15\times10 = 150kg\cdot m/s\)
Since the force and time - interval (implicitly the same for all as the same force is applied) are the same, the object with the largest initial momentum will have the greatest change in momentum in magnitude. Among the options, the object in option D has the largest initial momentum in the direction opposite to the applied force, so it will undergo the greatest change in momentum.

Answer:

D. A 15 kg object that is moving east at 10 m/s