A 75.0 kg stunt man jumps from a balcony and falls 28.0 m before colliding with a pile of mattresses. If the mattresses are compressed 0.800 m before he is brought to rest, what is the average force exerted by the mattresses on the stuntman?
force*distance=massman*g*heightfromabove
To find the average force exerted by the mattresses on the stuntman, we can use the concept of work and energy.
First, let's find the potential energy of the stuntman before he jumps:
Potential energy (PE) = mass (m) * gravity (g) * height (h)
PE = 75.0 kg * 9.8 m/s² * 28.0 m
Next, let's find the potential energy of the stuntman after he hits the mattresses:
PE = mass (m) * gravity (g) * height (h)
PE = 75.0 kg * 9.8 m/s² * 0.800 m
Since energy is conserved, the difference in potential energy will be equal to the work done by the mattresses:
Work done by the mattresses = PE before - PE after
Now let's calculate the average force:
Average force = Work done / Distance
The distance is the distance over which the force is exerted, which is the compression of the mattresses, given as 0.800 m.
Let's plug in the values into the equation:
Work done = PE before - PE after = (75.0 kg * 9.8 m/s² * 28.0 m) - (75.0 kg * 9.8 m/s² * 0.800 m)
Average force = (Work done) / (Compression distance) = (PE before - PE after) / (0.800 m)
Simplifying the calculation will give you the average force exerted by the mattresses on the stuntman.