Question.
A large truck and a car, both moving with a velocity of magnitude v, have a head-on collision.
If the collision lasts for 1 s
(a)Which vehicle experiences greater force of impact ?
(b)Which vehicle experiences greater change in momentum ?
(c)Which vehicle experiences greater acceleration ?
(d)Why is the car likely to suffer more damage than the truck ?
A large truck and a car, both moving with a velocity of magnitude v, have a head-on collision.
If the collision lasts for 1 s
(a)Which vehicle experiences greater force of impact ?
(b)Which vehicle experiences greater change in momentum ?
(c)Which vehicle experiences greater acceleration ?
(d)Why is the car likely to suffer more damage than the truck ?
Solution:
Let mass of truck $=\mathrm{M} ;$ mass of car $=\mathrm{m} ;$ velocity of truck $=\mathrm{v} ;$ time for which collision lasts,
$\mathrm{t}=1 \mathrm{~s} ;$ velocity of $\mathrm{car}=-\mathrm{V}$ (Negative sign for opposite direction of motion).
(a) On collision, both the vehicles experience the same force, as action and reaction are equal.
(b) Change in momentum of truck is equal and opposite to change in momentum of car, i.e.,
both the vehicles experience the same change in momentum.
(c) As acceleration = force / mass, and force on each vehicle is same, therefore,
acceleration $\propto \frac{1}{\text { mass }}$.
As mass of car is smaller, therefore, acceleration of car is greater than the acceleration of the truck.
(d) The car is likely to suffer more damage than the truck, as it is lighter. The acceleration i.e. change in velocity/time of car is more than that of the truck.
Let mass of truck $=\mathrm{M} ;$ mass of car $=\mathrm{m} ;$ velocity of truck $=\mathrm{v} ;$ time for which collision lasts,
$\mathrm{t}=1 \mathrm{~s} ;$ velocity of $\mathrm{car}=-\mathrm{V}$ (Negative sign for opposite direction of motion).
(a) On collision, both the vehicles experience the same force, as action and reaction are equal.
(b) Change in momentum of truck is equal and opposite to change in momentum of car, i.e.,
both the vehicles experience the same change in momentum.
(c) As acceleration = force / mass, and force on each vehicle is same, therefore,
acceleration $\propto \frac{1}{\text { mass }}$.
As mass of car is smaller, therefore, acceleration of car is greater than the acceleration of the truck.
(d) The car is likely to suffer more damage than the truck, as it is lighter. The acceleration i.e. change in velocity/time of car is more than that of the truck.
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.