Question 5 A large truck and a car, both moving with a velocity of magnitude v, have a head-on collision and both of them come to a halt after that. If the collision lasts for 1 s: (a) Which vehicle experiences the greater force of impact? (b) Which vehicle experiences the greater change in momentum? (c) Which vehicle experiences the greater acceleration? (d)Why is the car likely to suffer more damage than the truck?
Class 9 - Science - Force and Laws of Motion Page 130
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Let mass of truck = M
mass of car = m
velocity of truck = V
then, velocity of car = - V { because both are moving in opposite direction}
external force = 0
we know, according to 2nd Law of motion , if external force is equal to zero then, linear momentum will be conserved.
and also we know, according to 3rd Law of motion " action and reaction are of equal magnitude and directed in opposite directions "
(a) so , according to " 3rd Law of motion ". both experience equal magnitude of force .
(b) due to "conservation of Linear momentum " , both have same change in momentum .
(c) acceleration depends upon mass of body , and it is inversely proportional to mass . so, acceleration of car is greater then truck .
(d) due to acceleration of car is higher then truck .
mass of car = m
velocity of truck = V
then, velocity of car = - V { because both are moving in opposite direction}
external force = 0
we know, according to 2nd Law of motion , if external force is equal to zero then, linear momentum will be conserved.
and also we know, according to 3rd Law of motion " action and reaction are of equal magnitude and directed in opposite directions "
(a) so , according to " 3rd Law of motion ". both experience equal magnitude of force .
(b) due to "conservation of Linear momentum " , both have same change in momentum .
(c) acceleration depends upon mass of body , and it is inversely proportional to mass . so, acceleration of car is greater then truck .
(d) due to acceleration of car is higher then truck .
abhi178:
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Let the mass of the truck be M and that of the car be m and their initial velocity be v.
→ M > m
Let the final velocity of both vehicles be v′.
Given that both vehicles come to rest after collision, i.e. v’ = 0
Time of impact, t = 10 s
a. From Newton's second law of motion, the net force experienced by each vehicle is given by the relation:
Fcar = m (v′ − v)/t = mv/10
Ftrack = M (v′ − v)/t = −Mv/10
since the mass of the truck is greater than that of the car, it will experience a greater force of impact.
b. Initial momentum of the car = mv
Final momentum of the car = 0
Change in momentum = mv
Initial momentum of the truck = Mv
Final momentum of the truck = 0
Change in momentum = Mv
Mass of the truck is greater than that of the car. Thus, the truck will experience a greater change in momentum as compared to the car.
d. According to Newton's third law of motion, for every action, there is an equal and opposite reaction which acts on different bodies. Since the truck experiences a greater force of impact (the action force), this large impact force is also experienced by the car as a reaction force. Thus, the car is likely to suffer more damage than the truck.
→ M > m
Let the final velocity of both vehicles be v′.
Given that both vehicles come to rest after collision, i.e. v’ = 0
Time of impact, t = 10 s
a. From Newton's second law of motion, the net force experienced by each vehicle is given by the relation:
Fcar = m (v′ − v)/t = mv/10
Ftrack = M (v′ − v)/t = −Mv/10
since the mass of the truck is greater than that of the car, it will experience a greater force of impact.
b. Initial momentum of the car = mv
Final momentum of the car = 0
Change in momentum = mv
Initial momentum of the truck = Mv
Final momentum of the truck = 0
Change in momentum = Mv
Mass of the truck is greater than that of the car. Thus, the truck will experience a greater change in momentum as compared to the car.
d. According to Newton's third law of motion, for every action, there is an equal and opposite reaction which acts on different bodies. Since the truck experiences a greater force of impact (the action force), this large impact force is also experienced by the car as a reaction force. Thus, the car is likely to suffer more damage than the truck.
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