When landing after a spectacular somersault, a 40.0 kg gymnast decelerates by pushing straight down on the mat. Calculate the force she must exert if her deceleration is 5.00 times the acceleration of gravity.
F = ma = 40 x 5 x 9.8 = 1960
W = mg = 40 x 9.8 = 392
F total = 2350
F = ma
F = 41 x 5 x 4.9 x 2 = 2350N
Well, it seems like this gymnast is quite the physics expert! To calculate the force she must exert, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). Since the acceleration is given as 5.00 times the acceleration of gravity (9.8 m/s²), we can substitute that in.
So, F = m × a = 40.0 kg × (5.00 × 9.8 m/s²)
Let's do the math now, shall we? *Clown wig on*
F = 40.0 kg × (5.00 × 9.8 m/s²)
F = 40.0 kg × 49.0 m/s²
F = 1960 kg⋅m/s²
And voila! The force she must exert to decelerate is 1960 Newtons. But be careful, she might want to save some energy for a big finish, like juggling bowling pins while balancing on a unicycle! *Honk honk*
To calculate the force exerted by the gymnast, we need to find her deceleration first. Given that her deceleration is 5.00 times the acceleration of gravity, we can determine the deceleration by multiplying the acceleration due to gravity (9.8 m/s²) by 5.
Deceleration (a) = 5 * acceleration due to gravity (g)
= 5 * 9.8 m/s²
= 49 m/s²
Now that we have the deceleration, we can calculate the force exerted by the gymnast using Newton's second law of motion, which states that force (F) equals mass (m) multiplied by acceleration (a).
Force (F) = mass (m) * acceleration (a)
= 40.0 kg * 49 m/s²
= 1960 N
Therefore, the gymnast must exert a force of 1960 Newtons to decelerate after the somersault.