Question

3.3.2 test (cst): forces
question 18 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 10 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 5 m/s

Explanation:

Step1: Recall the impulse - momentum theorem

The impulse - momentum theorem states that \(J=\Delta p\), and \(J = F\Delta t\). Since the force \(F = 16\space N\) is applied for the same time \(\Delta t\) (not given, but the time of application is the same for all objects as the same force is applied to each object in the problem context) to each object, we can compare the change in momentum \(\Delta p\) based on the relationship \(J=\Delta p=F\Delta t\). However, if we consider the general form of momentum \(p = mv\) and assume a non - zero time of force application, we can also think about the fact that the object with the larger initial momentum (assuming the force acts for a non - zero time) will have a larger change in momentum (because \(\Delta p=F\Delta t\), and if we assume the force acts for a non - zero time, the object with the larger initial momentum will have a more significant change in its motion state).

Calculate the initial momentum \(p = mv\) for each object:

• For object A: \(p_A=m_Av_A=(20\space kg)\times(5\space m/s)=100\space kg\cdot m/s\)
• For object B: \(p_B=m_Bv_B=(15\space kg)\times(10\space m/s)=150\space kg\cdot m/s\)
• For object C: \(p_C=m_Cv_C=(20\space kg)\times(10\space m/s)=200\space kg\cdot m/s\)
• For object D: \(p_D=m_Dv_D=(15\space kg)\times(5\space m/s)=75\space kg\cdot m/s\)

Step2: Compare the initial momenta

Since \(p_D\lt p_A\lt p_B\lt p_C\) and using the impulse - momentum theorem \(J = F\Delta t=\Delta p\) (where \(F\) and \(\Delta t\) are the same for all objects). The object with the largest initial momentum (assuming the force acts for a non - zero time) will have the largest change in momentum.

Answer:

C. A 20 kg object that is moving east at 10 m/s