# 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 , the objects approach each other moving at velocities . The objects collide, and at a time they recede from each other moving at velocities , where and . The separation of the objects is the same at and . Which of the following properties of the system are different at and ?

• 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 , the objects approach each other moving at velocities . The objects collide and at a time , they recede from each other moving at velocities , where and . The separation of the objects is the same at and . Which of the following properties of the system are different at and ?

• 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 and , the positions of the objects are changed and the separations of each object are the same at and . At and , the objects are at rest. Which of the following properties of the system are different at and ?

• 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 , the objects approach each other, moving at velocities . At a time , the objects recede from each other, moving at velocities , where and . The separation of the objects is the same at and at . Which of the following properties of the system are different at and ?

• 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