A gymnast bounces on a trampoline - Edexcel - A-Level Physics - Question 15 - 2023 - Paper 1

To find the tension in the spring, we can resolve the vertical component of the tension, using:

$T_v = T imes ext{sin}( heta)$
where:

• $T_v = 68$ N (given vertical component of tension)
• $heta = 14°$

Rearranging gives:

T = rac{T_v}{ ext{sin}( heta)} = rac{68}{ ext{sin}(14°)}

Calculating the tension:

Using $ext{sin}(14°) ext{ approximately } 0.2419$,

T = rac{68}{0.2419} ext{ N} ext{ approximately } 281.3 ext{ N}

This shows that the tension is indeed near 300 N.

The stiffness of the spring (k) can be calculated using Hooke's Law, which relates the force exerted by the spring to its extension:

$F = k imes x$ Where:

• $F = T = 300 ext{ N}$ (approximately as calculated)
• $x = 4.6 imes 10^{-3} ext{ m}$ (extension of the spring)

Rearranging gives:

k = rac{F}{x} = rac{300}{4.6 imes 10^{-3}} ext{ N/m}

Calculating the stiffness:

$k ≈ 65109 ext{ N/m}$

Thus, the stiffness of the spring is approximately 65109 N/m.

While the gymnast is in contact with the trampoline, there are two primary forces acting on her:

1. Weight ($F_{weight}$): This force acts downwards due to gravity and is constant, given by the equation:
   $F_{weight} = m imes g$
   This represents the downward gravitational force on the gymnast.

2. Normal Contact Force ($F_{contact}$): This force acts upwards from the trampoline surface, opposing the weight.

   • The magnitude of the normal force changes as the gymnast moves.
   • When the gymnast is at the lowest point of her bounce, the normal force is at its maximum, noticeably greater than her weight, resulting in an upward net force. Therefore, the gymnast accelerates upwards.
   • As she moves upwards, the normal contact force decreases until it may become zero when she leaves the trampoline.
   • If the normal force is less than the weight, she would decelerate, and if it is greater, she accelerates.

Thus, the relationship between these two forces dictates her vertical acceleration—allowing her to bounce upwards when the normal force exceeds her weight, and resulting in downward acceleration when the normal force is less than her weight.