Question

6 the mass, velocity and kinetic energy for three vehicles are shown in the table below. a) order the vehicles from least momentum to greatest. show your work or explain your reasoning. b) suppose the car and van collide. as a result, the car comes to a complete stop after 0.8 s. determine the force of impact on the car. show y c) what is the force of impact on the van? show your work or explain your reasoning. d) determine the change momentum of the van as a result of the collision.

Explanation:

Part (a)

Step1: Recall momentum formula

Momentum \( p = mv \), where \( m \) is mass (kg) and \( v \) is velocity (m/s).

Step2: Calculate momentum for truck

For truck: \( m = 1900 \, \text{kg}, v = 16 \, \text{m/s} \)
\( p_{\text{truck}} = 1900 \times 16 = 30400 \, \text{kg·m/s} \)

Step3: Calculate momentum for car

For car: \( m = 1200 \, \text{kg}, v = 24 \, \text{m/s} \)
\( p_{\text{car}} = 1200 \times 24 = 28800 \, \text{kg·m/s} \)

Step4: Calculate momentum for van

For van: \( m = 1500 \, \text{kg}, v = 21 \, \text{m/s} \)
\( p_{\text{van}} = 1500 \times 21 = 31500 \, \text{kg·m/s} \)

Step5: Order by momentum

Compare \( p_{\text{car}} = 28800 \), \( p_{\text{truck}} = 30400 \), \( p_{\text{van}} = 31500 \).
Order: car (\( 28800 \)) < truck (\( 30400 \)) < van (\( 31500 \))

Step1: Recall impulse-momentum theorem

Force \( F = \frac{\Delta p}{\Delta t} \), where \( \Delta p = m\Delta v \), \( \Delta t = 0.8 \, \text{s} \).

Step2: Determine initial and final momentum of car

Initial momentum of car: \( p_{\text{initial}} = 1200 \times 24 = 28800 \, \text{kg·m/s} \)
Final momentum (stops): \( p_{\text{final}} = 0 \)
\( \Delta p = 0 - 28800 = -28800 \, \text{kg·m/s} \) (negative for direction, magnitude for force)

Step3: Calculate force

\( F = \frac{|\Delta p|}{\Delta t} = \frac{28800}{0.8} = 36000 \, \text{N} \)

Step1: Newton’s third law

Force on van is equal and opposite to force on car. From part (b), force on car is \( 36000 \, \text{N} \), so force on van is also \( 36000 \, \text{N} \) (opposite direction, same magnitude).

Answer:

car, truck, van

Part (b)