Question

three chairs were rolling across a flat office floor. the blue and red chairs are the same mass, and they have more mass than the yellow chair. each chair was hit by another chair, but not from the same direction. use the information in the diagram to answer. which chair(s) experienced the strongest force when hit? how do you know? blue chair: 12 kg (more mass) speed: 4 m/s speed: 1 m/s (slowed down by 3 m/s) red chair: 12 kg (more mass) speed: 3 m/s speed: 6 m/s (speeded up by 3 m/s) yellow chair: 10 kg (less mass) speed: 2 m/s speed: 5 m/s (speeded up by 3 m/s) the blue and red chairs experienced the strongest force because they are both more massive than the yellow chair and they changed speed by the same amount the red chair experienced the strongest force because it is as massive as the blue chair and has the highest ending speed. all three chairs experienced the same force because they changed speed by the same amount. the blue chair experienced the strongest force because it takes more force to slow an object than it takes to make it go faster.

Explanation:

Step1: Recall Newton's second - law

Force $F = ma$, where $m$ is mass and $a$ is acceleration. Acceleration $a=\frac{\Delta v}{\Delta t}$. Assuming the time of impact $\Delta t$ is the same for all chairs, we can compare forces by looking at the product of mass and change in velocity $\Delta v$.

Step2: Calculate change in velocity for each chair

Blue chair: Initial speed $v_i = 4$ m/s, final speed $v_f=1$ m/s, $\Delta v_{blue}=|1 - 4|=3$ m/s. Red chair: Initial speed $v_i = 3$ m/s, final speed $v_f = 6$ m/s, $\Delta v_{red}=|6 - 3|=3$ m/s. Yellow chair: Initial speed $v_i = 2$ m/s, final speed $v_f = 5$ m/s, $\Delta v_{yellow}=|5 - 2|=3$ m/s.

Step3: Compare forces using mass and $\Delta v$

Blue and red chairs have mass $m = 12$ kg, yellow chair has mass $m = 10$ kg. Since $F = m\Delta v$ and $\Delta v$ is the same for all chairs ($\Delta v=3$ m/s), and $m_{blue}=m_{red}>m_{yellow}$, the force on blue and red chairs is greater than the force on the yellow chair.

Answer:

The blue and red chairs experienced the strongest force because they are both more massive than the yellow chair and they changed speed by the same amount.