Newton's Second Law and Momentum Video Lessons

Concept

# Problem: Which of the following statements are true? Select all correct responses.a. The total momentum of any number of particles is equal to the vector sum of the momenta of the individual particles.b. The total momentum of any number of particles is equal to the algebraic sum of the momenta of the individual particles.c. The vector sum of forces acting on a particle equals the rate of change of momentum of the particle with respect to time.d. The total momentum of an isolated system is constant.e. The total momentum of any system is constant.f. The vector sum of forces acting on a particle equals the rate of change of velocity of the particle with respect to time.

###### FREE Expert Solution

We can better understand this problem by stating the law of conservation of momentum.

$\overline{)\begin{array}{rcl}{\mathbf{p}}_{\mathbf{i}}& {\mathbf{=}}& {\mathbf{p}}_{\mathbf{f}}\\ {\mathbf{m}}_{\mathbf{1}}{\mathbf{v}}_{\mathbf{1}\mathbf{i}}\mathbf{+}{\mathbf{m}}_{\mathbf{2}}{\mathbf{v}}_{\mathbf{2}\mathbf{i}}& {\mathbf{=}}& {\mathbf{m}}_{\mathbf{1}}{\mathbf{v}}_{\mathbf{1}\mathbf{f}}\mathbf{+}{\mathbf{m}}_{\mathbf{2}}{\mathbf{v}}_{\mathbf{2}\mathbf{f}}\end{array}}$

Also, we need Newton's second law of motion stating that the time rate of change of momentum is equal to the force acting on the particle.

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###### Problem Details

Which of the following statements are true? Select all correct responses.

a. The total momentum of any number of particles is equal to the vector sum of the momenta of the individual particles.
b. The total momentum of any number of particles is equal to the algebraic sum of the momenta of the individual particles.
c. The vector sum of forces acting on a particle equals the rate of change of momentum of the particle with respect to time.
d. The total momentum of an isolated system is constant.
e. The total momentum of any system is constant.
f. The vector sum of forces acting on a particle equals the rate of change of velocity of the particle with respect to time.