What is the magnitude of average force a pole vaulters exterts on a landing bag if it's 1.5 meters high and deforms by 0.5
M=60kg
Height of the bar=4.5m
His centre of mass is 1m
To calculate the magnitude of the average force exerted by the pole vaulter on the landing bag, we can use the principle of conservation of mechanical energy.
1. First, calculate the potential energy at the maximum height (mgh_max), where:
- m = mass of the pole vaulter (60 kg)
- g = acceleration due to gravity (9.8 m/s^2)
- h_max = maximum height (4.5 m)
Potential Energy (PE) = m * g * h_max
2. Next, calculate the potential energy at the height where the bag starts deforming (mgh_deform), where:
- h_deform = height of deformation (0.5 m)
Potential Energy (PE) = m * g * h_deform
3. The work done by the pole vaulter can be calculated by the difference in potential energy:
- Work Done = PE_max - PE_deform
4. The average force (F_avg) exerted by the pole vaulter on the landing bag can be calculated using the work-energy principle:
- Work Done = F_avg * d
- d = distance over which the force is applied (the deformation of the landing bag)
5. Rearrange the equation to solve for the average force:
- F_avg = Work Done / d
Substituting the calculated values, the solution will give you the magnitude of the average force exerted by the pole vaulter on the landing bag.