forces physics unit

Question

Kara (55 kg) is standing next to her brother Ben (80 kg) on a large piece of frictionless ice. Being a bit of a joker, Kara decides to push her brother with a force of 200 N expecting him to slide across the ice while she remains standing in the middle of the ice rink laughing. (8 marks)

1. Describe the motion that will actually be experienced by Kara and Ben. Imagine this scenario in your head first, then be sure to use appropriate vocabulary to describe the motion. Be sure to describe all parts of each person’s motion: beginning, middle, and end. 
2. Apply your knowledge of Newton’s Laws of Motion to explain why they undergo the motion described in part A.
3. What is Ben’s acceleration? What is Kara’s acceleration? Are they the same or different? Explain. 

Answer 1

1.

At the beginning both are motionless.

While Kara is applying force on Ben, Ben will be accelerating.

At the same time, Kara will experience the same force accelerating her

away from Ben.

When Kara stops applying force, both will continue moving away from each other

at their respective constant velocities (assuming no resistance).

2.

By Newton's Third Law, Kara will experience the same force as she is applying on Ben.

By Newton's second law, these two forces will cause both of them to accelerate.

By Newton's first law, as soon as the force stops, their velocities will not change.

3.

Let

m = 55 kg be Kara's mass,

M = 80 kg be Ben's mass,

F = 200 N be the force acting on both.

By Newton's second law

Ben's acceleration is F/M = 200/80 = 2.5 m/²

Kara's acceleration is is F/m = 200/55 ≈ 3.6 m/s²