a small car has a head-on collision with a large truck. Which vehicle has the larger change in momentum?
The force on the little one from the big one is the same as the force on the big one from the little one .
the time period is the same
so
force = rate of change of momentum =change of momentum/time = same for both because same force magnitude
To determine which vehicle has the larger change in momentum in a head-on collision between a small car and a large truck, we need to consider two factors: the mass and the initial velocity of each vehicle.
The momentum of an object is defined as the product of its mass and velocity. Mathematically, momentum (p) is given by the equation p = m * v, where m is the mass of the object and v is its velocity.
Since we know that the car and the truck collide head-on, we can assume they have opposite velocities, with the car moving in one direction and the truck moving in the opposite direction. Let's assume that the car's initial velocity is positive (moving in the positive direction), and the truck's initial velocity is negative (moving in the negative direction).
Now, to determine the change in momentum for each vehicle, we need to subtract their final momentum from their initial momentum. The initial momentum is given by the equation p_initial = m * v_initial, and the final momentum is given by the equation p_final = m * v_final.
Assuming the collision is perfectly inelastic (meaning the vehicles stick together and move as one mass after the collision), the final velocity (v_final) for both vehicles will be the same. Let's call this final velocity "vf."
For the small car, the initial momentum (p_initial_car) would be the product of its mass (m_car) and its initial velocity (v_initial_car). Assuming the car's mass is smaller than the truck's mass, we'll label it as m_car.
p_initial_car = m_car * v_initial_car
For the large truck, the initial momentum (p_initial_truck) would be the product of its mass (m_truck) and its initial velocity (v_initial_truck). Assuming the truck has a larger mass than the car, we'll label it as m_truck.
p_initial_truck = m_truck * v_initial_truck
After the collision, if the car and the truck stick together and move with the same final velocity (vf), both vehicles' final momentum would be:
p_final_car = (m_car + m_truck) * vf
p_final_truck = (m_car + m_truck) * vf
To determine which vehicle had the larger change in momentum, we need to compare the differences between the initial and final momenta for each vehicle:
Δp_car (change in momentum for the car) = p_final_car - p_initial_car
Δp_truck (change in momentum for the truck) = p_final_truck - p_initial_truck
Comparing the magnitudes of Δp_car and Δp_truck will tell us which vehicle had the larger change in momentum.