FIGURE EX11.6 is an incomplete momentum bar chart for a collision that lasts 10 ms. What are the magnitude and direction of the average collision force exerted on the object?

Verified step by step guidance

1. Identify the initial momentum (P_ix) from the bar chart. The initial momentum is 6 kg·m/s.
2. Identify the final momentum (P_fx) from the bar chart. The final momentum is -3 kg·m/s.
3. Calculate the change in momentum (ΔP) using the formula ΔP = P_fx - P_ix.
4. Use the impulse-momentum theorem, which states that the impulse (J_x) is equal to the change in momentum (ΔP).
5. Calculate the average collision force (F_avg) using the formula F_avg = J_x / Δt, where Δt is the duration of the collision (10 ms or 0.01 s).

Key Concepts

Momentum

Momentum is a vector quantity defined as the product of an object's mass and its velocity. It is represented mathematically as p = mv, where p is momentum, m is mass, and v is velocity. In collisions, momentum is conserved, meaning the total momentum before the collision equals the total momentum after the collision, provided no external forces act on the system.

Impulse

Impulse is the change in momentum of an object when a force is applied over a period of time. It is calculated as the product of the average force (F) and the time duration (Δt) during which the force acts, expressed as J = FΔt. Impulse is crucial in analyzing collisions, as it helps determine the force exerted during the interaction and is equal to the change in momentum.

Average Force

Average force is defined as the total impulse delivered to an object divided by the time duration over which the force acts. It can be calculated using the formula F_avg = J/Δt. In the context of collisions, understanding the average force helps in determining how much force was exerted on an object during the collision, which is essential for analyzing the effects of the collision on the objects involved.