Caitlyn L.

asked • 03/16/17# Impulse and force

## 2 Answers By Expert Tutors

Steven W. answered • 03/16/17

Physics Ph.D., college instructor (calc- and algebra-based)

Hi Caitlyn! Following my reasoning from the comment above, we can calculate the impulse on each vehicle by calculating its change in momentum from start to finish. By the impulse-momentum theorem, the value of the change in momentum and the value of the impulse should be equal. To get base units, we first need to convert the km/h to m/s and tonnes to kg. 105 km/h = 29.2 m/s 100 km/h = 27.8 m/s 3 tonnes = 3000 kg 1.5 tonnes = 1500 kg Hence, the change in momentum of the truck (defining the truck to be traveling in the positive direction) is: dp_truck = p_truck_f - p_truck_i = 0 - (3000 kg)(29.2 m/s) = -87,600 kg*m/s (or N*s) Then: dp_car = 0 - (1500 kg)(-27.8 m/s) = 41,700 kg*m/s (or N*s) [note: the car is traveling in the negative direction if the truck is going in the positive direction; unless they specify a positive direction for you, they may only be concerned about the magnitudes of these answers, not the signs] We are told this entire process takes 0.3 s. Since impulse = force * time, force = impulse/time. Hence, for the car: F_net = impulse_car/time = 41,700/0.3 = 139,000 N Arturo is exactly right, by the way, that this question is horridly phrased (as presented here, at least). It makes it sound as if the vehicles come to rest immediately after the collision, due only to the force of each vehicle on the other. This would violate conservation of momentum, and could not happen. And 0.3 seconds is a very short time for what I described to happen. Nonetheless, this is a possibility. I hope it helps you out! And if you have any other questions, just let me know.

Arturo O. answered • 03/16/17

Experienced Physics Teacher for Physics Tutoring

_{i}= initial speed of truck (given)

_{f}= final speed of truck = 0 (assume it came to a full stop due only to the collision)

_{1}= impulse = change in momentum = Mv

_{f}- Mv

_{i}

_{1}= M·(0) - Mv

_{f}= -Mv

_{f}

_{1}= force = I/t = -Mv

_{f}/ t

_{1}and F

_{1}, but first convert to consistent units.

_{i}= initial speed of car (given, but use a negative sign, assuming it is moving to the left)

_{f}= final speed of car = 0

_{2}= -mu

_{i }(comes out positive since u

_{i}is negative)

_{2}= -mu

_{i}/t

_{1}should equal -F

_{2}, but it does not come out that way under the stated conditions of the problem.

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Arturo O.

03/16/17