A bungee jumper (m = 66.00 kg) tied to a 39.00 m cord, leaps off a 69.00 m tall bridge. He falls to 5.00 m above the water before the bungee cord pulls him back up. What size impulse is exerted on the bungee jumper while the cord stretches?
To determine the size of the impulse exerted on the bungee jumper while the cord stretches, we need to use the principle of conservation of mechanical energy.
1. First, we need to calculate the potential energy of the bungee jumper at the top of the bridge before falling. The potential energy (PE) is given by the formula: PE = mass (m) * gravity (g) * height (h). In this case, the mass is 66.00 kg, gravity is approximately 9.8 m/s^2, and the height is 69.00 m. So, the potential energy at the top is: PE = 66.00 kg * 9.8 m/s^2 * 69.00 m.
2. Once the bungee jumper reaches the lowest point, 5.00 m above the water, the potential energy is converted into kinetic energy (KE). The kinetic energy is given by the formula: KE = 0.5 * mass (m) * velocity^2 (v^2). At the lowest point, the velocity is zero because the bungee jumper briefly stops before being pulled back up by the bungee cord. So the kinetic energy is zero as well.
3. Since we assume no energy is lost due to air resistance or other factors, the mechanical energy is conserved throughout the motion. Therefore, the potential energy at the top is equal to the potential energy at the lowest point: PE = KE.
4. From step 1, we have the expression for potential energy at the top. From step 2, we have the expression for kinetic energy at the lowest point. Equating them, we get: m * g * h = 0.5 * m * v^2.
5. Rearranging the equation, we can solve for velocity (v): v = sqrt(2 * g * h). Plug in the values of g (9.8 m/s^2) and h (5.00 m) to calculate the velocity.
6. With the velocity of the bungee jumper at the lowest point, we can now calculate the impulse exerted on the bungee jumper while the cord stretches. Impulse (I) is defined as the change in momentum and can be found using the formula: I = m * ∆v, where ∆v is the change in velocity.
7. In this case, ∆v is the final velocity (0 m/s, when the bungee jumper stops at the lowest point) minus the initial velocity (found in step 5). Plug in the values of the mass (66.00 kg) and the initial and final velocities to calculate the impulse exerted on the bungee jumper while the cord stretches.
By following these steps, you can find the size of the impulse exerted on the bungee jumper.