Worksheet: Systems of Objects

In this worksheet, we will practice analyzing the changes in the properties of systems of objects and the forces involved in such changes.

Q1:

A system consists of two identical objects, as shown in the diagram. The objects exert repulsive forces on each other. At a time 𝑡, the objects approach each other moving at velocities vv=. The objects collide, and at a time 𝑡 they recede from each other moving at velocities vv=, where vv> and vv>. The separation of the objects is the same at 𝑡 and 𝑡.

Which of the following properties of the system are different at 𝑡 and 𝑡?

  • AVelocity of the center of mass
  • BNo properties of the system change.
  • CKinetic energy
  • DPotential energy
  • ELinear momentum

Which of the following types of forces explains any changes to the system?

  • ANo forces
  • BInternal forces alone
  • CExternal forces alone
  • DBoth internal and external forces

Q2:

A system consists of two identical objects, as shown in the diagram. The objects exert repulsive forces on each other. At a time 𝑡, the objects approach each other moving at velocities vv=. The objects collide and at a time 𝑡, they recede from each other moving at velocities vv=, where vv= and vv=. The separation of the objects is the same at 𝑡 and 𝑡.

Which of the following properties of the system are different at 𝑡 and 𝑡?

  • ALinear momentum
  • BVelocity of the center of mass
  • CPotential energy
  • DKinetic energy
  • ENo properties of the system change.

Which of the following types of forces explains any changes to the system?

  • AExternal forces alone
  • BInternal forces alone
  • CNo forces
  • DBoth internal and external forces

Q3:

A system consists of four identical objects, as shown in the diagram. The objects exert both attractive and repulsive forces on each other that result in a zero net force exerted on each object. Between times 𝑡 and 𝑡, the positions of the objects are changed and the separations of each object are the same at 𝑡 and 𝑡. At 𝑡 and 𝑡, the objects are at rest.

Which of the following properties of the system are different at 𝑡 and 𝑡?

  • AKinetic energy
  • BAngular momentum
  • CPotential energy
  • DNo properties of the system change.
  • ELinear momentum

Which of the following types of forces explain any changes to the system?

  • ANo forces
  • BBoth internal and external forces
  • CInternal forces alone
  • DExternal forces alone

Q4:

A system consists of two identical objects, as shown in the diagram. The objects exert negligible forces on each other. At a time 𝑡, the objects approach each other, moving at velocities vv=. At a time 𝑡, the objects recede from each other, moving at velocities vv=, where vv= and vv=. The separation of the objects is the same at 𝑡 and at 𝑡.

Which of the following properties of the system are different at 𝑡 and 𝑡?

  • APotential energy
  • BNo properties of the system change.
  • CLinear momentum
  • DVelocity of the center of mass
  • EKinetic energy

Which of the following types of forces explains any changes to the system?

  • ANo forces are required to explain the changes to the system.
  • BBoth internal and external forces are required to explain the changes to the system.
  • CInternal forces alone
  • DExternal forces alone

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