Impulse and force

Question

I've been stuck on this question forever and I keep getting it wrong :( Please help!

 

A truck of mass 3 tonnes is travelling at 105km/h when it hits a car of mass 1.5 tonne travelling in the opposite direction at 100km/h. The collision takes place for 0.3 seconds and after it both the car and the truck come to rest.

 

a) Calculate the Impulse felt by the truck and the car

*For this question, the hint given to me was that the impulse for both needed to be calculated separately

 

b) Calculate the force felt by the car.

 

Thank you so much!

Answer 1

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.

Answer 2

Steven is correct that there must be other forces at work in this problem, which are not stated.  Otherwise, there would be violations of momentum conservation and Newton's 3rd law.  But let us assume for the sake of argument that the truck comes to a full stop due only to the collision with the car.

 

For the truck:

 

 

M = mass of truck (given)

v_i = initial speed of truck (given)

v_f = final speed of truck = 0 (assume it came to a full stop due only to the collision)

t = time interval over which the force acts (given)

I₁ = impulse = change in momentum = Mv_f - Mv_i

 

I₁ = M·(0) - Mv_f = -Mv_f

 

F₁ = force = I/t = -Mv_f / t

 

Plug in the numbers to get I₁ and F₁, but first convert to consistent units.

 

For the car:

 

Do the same analysis.

 

m = mass of car (given)

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

u_f = final speed of car = 0 

t = time interval over which the force acts (given)

 

Then

 

I₂ = -mu_i (comes out positive since u_i is negative)

 

Now here is the problem.  In addition to momentum conservation, Newton's 3rd law has to hold.  The force on the car is 

 

F₂ = -mu_i/t

 

By Newton's 3rd law, F₁ should equal -F₂, but it does not come out that way under the stated conditions of the problem.