Question

based on your results, newtons third law
applies in elastic collisions, regardless of how
the objects masses compare.

use the square counterclockwise arrow button
to reset the objects positions. set the mass of
object 1 to 1.00 kg and the \elasticity\ slider to
0%. press play to observe an inelastic collision
where the two objects stick together.

assuming the collision lasts 0.01 s, calculate
the acceleration and force experienced by
each object. enter your answers in the boxes.

object	( m ) (kg)	( v_{x, \text{initial}} ) (( \frac{\text{m}}{\text{s}} ))	( v_{x, \text{final}} ) (( \frac{\text{m}}{\text{s}} ))	( a ) (( \frac{\text{m}}{\text{s}^2} ))	( f ) (n)
2	1.50	(-0.50)	(square)	(square)	(square)

Explanation:

Step 1: Find final velocity (inelastic collision)

For inelastic collision, momentum is conserved: \( m_1v_{1i} + m_2v_{2i} = (m_1 + m_2)v_f \)
\( m_1 = 1.00 \, \text{kg}, v_{1i} = 1.00 \, \text{m/s}, m_2 = 1.50 \, \text{kg}, v_{2i} = -0.50 \, \text{m/s} \)
\( (1.00)(1.00) + (1.50)(-0.50) = (1.00 + 1.50)v_f \)
\( 1.00 - 0.75 = 2.50v_f \)
\( 0.25 = 2.50v_f \)
\( v_f = \frac{0.25}{2.50} = 0.10 \, \text{m/s} \) (same for both objects)

Step 2: Calculate acceleration for Object 1

Acceleration formula: \( a = \frac{v_f - v_{i}}{t} \)
\( v_f = 0.10 \, \text{m/s}, v_{i} = 1.00 \, \text{m/s}, t = 0.01 \, \text{s} \)
\( a_1 = \frac{0.10 - 1.00}{0.01} = \frac{-0.90}{0.01} = -90 \, \text{m/s}^2 \)

Step 3: Calculate force for Object 1

Force formula: \( F = ma \)
\( m_1 = 1.00 \, \text{kg}, a_1 = -90 \, \text{m/s}^2 \)
\( F_1 = (1.00)(-90) = -90 \, \text{N} \)

Step 4: Calculate acceleration for Object 2

\( v_f = 0.10 \, \text{m/s}, v_{i} = -0.50 \, \text{m/s}, t = 0.01 \, \text{s} \)
\( a_2 = \frac{0.10 - (-0.50)}{0.01} = \frac{0.60}{0.01} = 60 \, \text{m/s}^2 \)

Step 5: Calculate force for Object 2

\( m_2 = 1.50 \, \text{kg}, a_2 = 60 \, \text{m/s}^2 \)
\( F_2 = (1.50)(60) = 90 \, \text{N} \) (Note: Forces should be equal and opposite, \( F_1 = -F_2 \), which checks out)

Filling the table:

Object	\( m \, (\text{kg}) \)	\( v_{x, \text{initial}} \, (\frac{\text{m}}{\text{s}}) \)	\( v_{x, \text{final}} \, (\frac{\text{m}}{\text{s}}) \)	\( a \, (\frac{\text{m}}{\text{s}^2}) \)	\( F \, (\text{N}) \)
2	1.50	-0.50	0.10	60	90

(If only numerical answers for each box in order: Object 1 final velocity: 0.10, acceleration: -90, force: -90; Object 2 final velocity: 0.10, acceleration: 60, force: 90)

Answer:

Step 1: Find final velocity (inelastic collision)

For inelastic collision, momentum is conserved: \( m_1v_{1i} + m_2v_{2i} = (m_1 + m_2)v_f \)
\( m_1 = 1.00 \, \text{kg}, v_{1i} = 1.00 \, \text{m/s}, m_2 = 1.50 \, \text{kg}, v_{2i} = -0.50 \, \text{m/s} \)
\( (1.00)(1.00) + (1.50)(-0.50) = (1.00 + 1.50)v_f \)
\( 1.00 - 0.75 = 2.50v_f \)
\( 0.25 = 2.50v_f \)
\( v_f = \frac{0.25}{2.50} = 0.10 \, \text{m/s} \) (same for both objects)

Step 2: Calculate acceleration for Object 1

Acceleration formula: \( a = \frac{v_f - v_{i}}{t} \)
\( v_f = 0.10 \, \text{m/s}, v_{i} = 1.00 \, \text{m/s}, t = 0.01 \, \text{s} \)
\( a_1 = \frac{0.10 - 1.00}{0.01} = \frac{-0.90}{0.01} = -90 \, \text{m/s}^2 \)

Step 3: Calculate force for Object 1

Force formula: \( F = ma \)
\( m_1 = 1.00 \, \text{kg}, a_1 = -90 \, \text{m/s}^2 \)
\( F_1 = (1.00)(-90) = -90 \, \text{N} \)

Step 4: Calculate acceleration for Object 2

\( v_f = 0.10 \, \text{m/s}, v_{i} = -0.50 \, \text{m/s}, t = 0.01 \, \text{s} \)
\( a_2 = \frac{0.10 - (-0.50)}{0.01} = \frac{0.60}{0.01} = 60 \, \text{m/s}^2 \)

Step 5: Calculate force for Object 2

\( m_2 = 1.50 \, \text{kg}, a_2 = 60 \, \text{m/s}^2 \)
\( F_2 = (1.50)(60) = 90 \, \text{N} \) (Note: Forces should be equal and opposite, \( F_1 = -F_2 \), which checks out)

Filling the table:

Object	\( m \, (\text{kg}) \)	\( v_{x, \text{initial}} \, (\frac{\text{m}}{\text{s}}) \)	\( v_{x, \text{final}} \, (\frac{\text{m}}{\text{s}}) \)	\( a \, (\frac{\text{m}}{\text{s}^2}) \)	\( F \, (\text{N}) \)
2	1.50	-0.50	0.10	60	90

(If only numerical answers for each box in order: Object 1 final velocity: 0.10, acceleration: -90, force: -90; Object 2 final velocity: 0.10, acceleration: 60, force: 90)