A 1600 kg car moving at 22 m/s is in a wreck with a 2900 truck moving at 32 m/s in the opposite direction. Which exerts a greater magnitude of force on the other?
In the instant of the collision, newton's third law says that each exerts an equal force on the other. Newton's second law, however, says that the acceleration of each is equal to that reaction force divided by the object's mass.
To determine which vehicle exerts a greater magnitude of force on the other, we can calculate the change in momentum for both vehicles.
The change in momentum (Δp) is given by the formula:
Δp = (mass × final velocity) - (mass × initial velocity)
For the car:
Mass of the car (m₁) = 1600 kg
Initial velocity of the car (v₁) = 22 m/s
Final velocity of the car (v₁f) = ?
Δp₁ = (m₁ × v₁f) - (m₁ × v₁)
For the truck:
Mass of the truck (m₂) = 2900 kg
Initial velocity of the truck (v₂) = 32 m/s
Final velocity of the truck (v₂f) = ?
Δp₂ = (m₂ × v₂f) - (m₂ × v₂)
The magnitude of force is directly proportional to the change in momentum.
Therefore, we need to compare the magnitudes of Δp₁ and Δp₂ to determine which one is larger.
To determine which vehicle exerts a greater magnitude of force on the other, we need to calculate the force generated during the collision.
The force experienced during a collision can be calculated using Newton's second law of motion, which states that force is equal to the rate of change of momentum.
The momentum of an object is defined as the product of its mass and velocity. Therefore, the momentum of the car can be calculated as mass of the car (m1) multiplied by its velocity (v1), and the momentum of the truck can be calculated as the mass of the truck (m2) multiplied by its velocity (v2).
The momentum (p) of an object is given by the formula:
p = m * v
Now, let's calculate the momentum for both the car and the truck:
Momentum of the car = mass of car * velocity of car
= 1600 kg * 22 m/s
= 35200 kg·m/s
Momentum of the truck = mass of truck * velocity of truck
= 2900 kg * 32 m/s
= 92800 kg·m/s
Next, using the principle of conservation of momentum, we can determine the total momentum before and after the collision. In a collision where no external forces are acting, the total momentum before the collision is equal to the total momentum after the collision.
Since the car and the truck are moving in opposite directions, the net momentum before the collision is the difference between the momentum of the truck and the momentum of the car:
Net momentum before collision = momentum of truck - momentum of car
= 92800 kg·m/s - 35200 kg·m/s
= 57600 kg·m/s
Since the total momentum before the collision is equal to the total momentum after the collision, the net momentum after the collision is also 57600 kg·m/s.
Now, the force exerted on an object can be calculated using the formula:
Force = (Change in momentum) / (Time)
In this case, we do not have the time of the collision, but we can compare the magnitudes of the forces by comparing the change in momentum.
Since the net momentum before and after the collision is the same, the change in momentum is zero. Therefore, the force exerted on both the car and the truck during the collision is equal in magnitude.