Use Force Analysis to identify all Action-Reaction (Newton’s 3rd Law) Pairs and identify any forces that are equal in magnitude.
Activity5.5.2.A*R*C*S: Uh-Oh Dr. Paws.
The instructor pushes a footstool (mass \(m_1\)) across the floor with a constant force so that the footstool speeds up. Dr. Paws (a dog with mass \(m_2\)) is sitting on the footstool. The coefficient of static friction between the dog and footstool is \(\mu\) (assume no friction with the ground).
Figure5.5.2.A simplified sketch of a dog on a footstool.
(a)1. Analyze and Represent.
In the example that follows, describe why the assumptions are reasonable, identify all Action-Reaction (Newton’s 3rd Law) Pairs, and identify and fix the problems with the free-body diagrams.
List quantities.
Mass of the footstool: \(m_1 = 10 \mathrm{~kg}\)
Mass of the dog: \(m_2 = 30 \mathrm{~kg}\)
Coefficient of static friction: \(\mu = 0.4\)
Instructor force: \(F_i = ?\)
Identify assumptions.
Near-earth: \(g = 10 \mathrm{~m/s^2}\text{;}\) particle-model; neglect air-resistance; no friction with the ground.
Represent the situation physically.
Figure5.5.3.Two free-body diagrams.
(b)3. Sensemake.
You have three friends who each calculate a different equation for the maximum allowable force the instructor can apply:
Use a sensemaking strategy to give a reason why each expression is incorrect.
(c)2. Calculate.
Represent physics principles that will help you solve for the tension and the acceleration.
Determine a symbolic equation for each unknown quantity in terms of known variables.
Plug numbers into your symbolic answer.
Activity5.5.3.The Block Race.
Block A is accelerated across a frictionless table by a hanging \(10 \mathrm{~N}\) mass. An identical block B is accelerated by a constant \(10 \mathrm{~N}\) tension in the string.
Figure5.5.4.Two Blocks connected to strings.
(a)
Before you begin, predict which block you think will have a larger acceleration.
(b)
Use Force Analysis to determine the acceleration of each block. Sketching free-body diagrams for each object is essential!
Activity5.5.4.The Pair of Blocks.
Blocks A and B are connected by an ideal string via a massless pulley. The coefficient of kinetic friction is \(\mu\text{.}\)
Figure5.5.5.Two Blocks connected by a string over a pulley.
Use the A*R*C*S Steps to determine the acceleration of each block.
This situation is a particularly good one for special-case analysis: what are some cases you might want to try?
Activity5.5.5.The Pair of Pulleys.
Blocks A and B are connected by an ideal string via two massless pulleys.
Figure5.5.6.Two Blocks connected by a string to two pulleys.
Use the A*R*C*S Steps to determine the acceleration of each block.