A small guy moving at a high speed collides with a stationary large football player. Now, which person experiences the larger force during the collision?
how and why?
According to Newton's third law of motion, the force exerted on an object is equal to the force that the object exerts back. In this case, the small guy and the stationary football player will experience equal and opposite forces during the collision.
The magnitude of the forces depends on the change in momentum. Momentum is the product of an object's mass and velocity. Since the small guy is moving at a high speed, he has a larger momentum compared to the stationary football player. When they collide, the small guy's momentum will change due to the interaction, leading to a larger force experienced by the small guy.
On the other hand, the large football player's momentum will change significantly less because of his larger mass and initial stationary position. Therefore, he will experience a smaller force compared to the smaller guy in this collision.
To determine which person experiences a larger force during the collision, we can apply Newton's second law of motion, which states that force is equal to the rate of change of momentum. Momentum is the product of mass and velocity, and it is conserved in a collision.
Let's assume the small guy has a mass of m1 and a velocity of v1 before the collision, while the large football player has a mass of m2 and is initially stationary (velocity v2 = 0).
Before the collision, the momentum of the small guy is given by p1 = m1 * v1. Since the football player is stationary, their momentum is initially p2 = m2 * v2 = 0.
After the collision, let's assume both individuals move together with a final velocity of vf. By applying the principle of conservation of momentum, we have:
p1 + p2 = (m1 * v1) + (m2 * v2) = (m1 + m2) * vf
Since both individuals remain in contact and move together, their final velocity is the same (vf) and equal to the velocity of the collision. Therefore:
(m1 + m2) * vf = m1 * v1
To compare the forces experienced by the small guy and the football player, we need to consider impulse. Impulse is given by the change in momentum and can be calculated by multiplying the force by the time interval over which the force acts.
Since both individuals experience the same change in momentum, the impulse they experience is the same. However, since the collision time is likely very short, the force experienced by each person will depend on this interval.
Typically, the smaller person will experience a larger force during the collision. This is due to the fact that force is directly proportional to the rate of change of momentum (force = Δp / Δt). Since the change in momentum is the same for both individuals, a smaller person will likely experience a larger force as the time interval over which the force acts for them is smaller.