Question

In a study conducted by a University of Illinois researcher, the football team at Unity High School in Tolono, IL was equipped for an entire season with helmets containing accelerometers. Information about every impact in practice and in games was sent to a computer present on the sidelines. The study found that the average force on a top of the head impact was 1770 N. If the initial velocity of the head was 2.09 m/s and the collision brings the head to a stop, and assuming the head has a mass of 4.12 kg, determine the duration of the impact.
(Note: we are treating the head as a free body which is a bit of an approximation).

Answer 1

The duration (i.e time) of the impact, given that the head impact was 1770 N is 0.005 s

How do I determine the duration (i.e time)?

Impulse is defined as the change in momentum of an object. It is expressed as:

Impulse = change in momentum

Impulse = final momentum – Initial momentum

Impule = m(v - u)

Impulse = force × time

Impulse = Ft

Thus,

Ft = m(v - u)

Where

• F is the force
• t is the time
• m is the mass
• u is the initial velocity
• v is the final velocity

Now, we can obtain the duration (i.e time) of the impact. Details below:

• Force (F) = 1770 N
• Initial velocity = 2.09 m/s
• Mass (m) = 4.12 Kg
• Final velocity = 0 m/s
• Duration (t) =?

Ft = m(v + u) since the collision came to a stop

1770 × t = 4.12 × (0 + 2.09)

1770 × t = 4.12 × 2.09

Divide both sides by 1770

t = (4.12 × 2.09) / 1770

t = 0.005 s

Thus, the duration is 0.005 s

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