Proving and Explaining Impulse Approximation

Summary

In this lesson, the instructor explores the force of impact on the body when landing after stepping off a wall, comparing scenarios where the knees are bent versus not bent. Using the impulse approximation, which assumes the impact force dominates other forces, the net force is calculated for both cases. The analysis reveals that while the impulse approximation works well in scenarios with very short collision times, it introduces significant errors when the collision duration is longer. The lesson highlights the importance of time duration in calculating impact forces and the accuracy of approximations in different situations.

Takeaways

• 😀 The force of impact on the body when bending the knees was 988.03 N (roughly 990 N), while not bending the knees resulted in a force of 11,065.93 N (roughly 11,000 N).
• 😀 The net force during a collision is approximately equal to the force of impact, as other forces are negligible during the short time interval of the collision.
• 😀 The impulse approximation states that the impact force is significantly larger than other forces acting on the body during a collision, making other forces negligible.
• 😀 The force of gravity acts downward, while the force from the ground (normal force) acts upward, balancing each other out during the collision.
• 😀 The normal force is the force of impact, which can be calculated by adding the net force and the force of gravity acting on the body.
• 😀 The equation to calculate force normal (impact force) is: normal force = net force + force of gravity.
• 😀 The force of gravity is calculated using the equation: mass × acceleration due to gravity (9.81 m/s²).
• 😀 In the bent knee case, the total normal force (impact force) was 1704.16 N, and in the not bent knee case, it was 11,782.06 N.
• 😀 The relative error equation can be used to determine the accuracy of the impulse approximation by comparing the observed value to the accepted value.
• 😀 The impulse approximation produced a large error of -42% in the bent knee case, suggesting it was not accurate enough to use in this scenario.
• 😀 In the not bent knee case, the impulse approximation produced a smaller error of about -6%, showing that shorter collision times lead to more accurate approximations.

Q & A

What is the impulse approximation and how does it relate to force of impact?

The impulse approximation assumes that during short-time collisions, the force of impact is significantly larger than other forces acting on the body, making the net force approximately equal to the force of impact. This simplification helps in calculating the force of impact during collisions, but it may not always be accurate if the collision time is longer.

How does bending your knees affect the force of impact when stepping off a wall?

Bending your knees increases the time of collision with the ground, which in turn reduces the force of impact. This happens because a longer collision time reduces the rate at which momentum is transferred, decreasing the magnitude of the force experienced.

What is the net force acting on the body during a collision?

The net force during a collision is the sum of the normal force (the force exerted by the ground) and the gravitational force (the force pulling the body down). The normal force is considered the force of impact during the collision.

What forces are acting on the body during the collision?

During the collision, two main forces act on the body: the force of gravity (acting downwards) and the normal force (acting upwards, which is equal to the force of impact).

How do you calculate the normal force during a collision?

To calculate the normal force, you sum the net force acting on the body with the gravitational force. The equation is: Normal Force = Net Force + Force of Gravity.

What is the significance of the relative error calculation in this lesson?

The relative error calculation is used to assess the accuracy of the impulse approximation. A larger error indicates that the approximation may not be suitable for the given scenario. For example, a relative error of -42% in the bent-knee case shows that the approximation is not very accurate when the collision time is relatively long.

What was the relative error for the bent knee and not bent knee scenarios?

The relative error for the bent knee case was approximately -42%, indicating a large error, while the relative error for the not bent knee case was about -6.1%, showing a smaller but still noticeable error.

Why does the time of collision matter in the impulse approximation?

The time of collision affects the accuracy of the impulse approximation. When the collision time is very short, the force of impact becomes much larger compared to other forces, making the approximation more accurate. Longer collision times lead to smaller forces of impact and a less accurate approximation.

What role does gravity play in determining the net force during a collision?

Gravity contributes to the net force during a collision by pulling the body downwards. The normal force, which counteracts gravity, is responsible for the force of impact. The net force is the sum of these two forces, with gravity pulling down and the normal force pushing up.

How did the time of collision differ between the bent-knee and not bent-knee cases?

In the bent-knee case, the collision time was 0.28 seconds, whereas in the not bent-knee case, the collision time was much shorter at 0.025 seconds. This difference in time affects the magnitude of the force of impact, with the shorter time resulting in a higher force.