I'm not quite sure how the formula works. I thought it was 55*6*9.81 = N
Weight * acceleration * gravity = N
My answer was wrong. Could anyone help me understand this question, please?

"When landing after a spectacular somersault, a 55.0 kg gymnast decelerates by pushing straight down on the mat. Calculate the force (in N) she must exert if her deceleration is 6.00 times the acceleration of gravity."

See the explanation below.

Explanation:

Of course yes, after my explanation you will understand very well how to analyze this type of problems.

First, we must differentiate the weight of the mass, the mass has units of kilograms or pounds, while the weight is the product of the mass by gravitational acceleration. In this way, we have the following formula for the weight of anybody.

w = m*g

where:

w = weight [N] (units of Newtons]

m = mass [kg]

g = gravity acceleration = 9.81 [m/s²]

When we have the product of these units [kg]*[m/s²], We are always going to get as a result the units of Newtons [N], The Newton is a unit of force.

Now, to solve this problem we must use Newton's second law, which tells us that the sum of forces on a body must be equal to the product of mass by acceleration.

ΣF = m*a

where:

ΣF  = forces acting over the gymnast [N]

m = mass = 55 [kg]

a = desacceleration = 6*9.81 = 58.86 [m/²]

Now we have two forces acting over the gymnast the first one is his or her weight (the mass by the gravity acceleration) and the second force is the one made it by his or her legs upwards in order to be standing. Let's take as positive signs the movements and forces upwards and negative downwards

- (m*g) + Fl = m*a

where:

Fl = force made it by the legs [N]

As the deceleration is upward because it prevents the person from continuing to go down, it is taken as a positive sign.

- (55*9.81) + Fl = (55*58.86)

Fl =  (55*58.86) + (55*9.81)

Fl = 3776.85 [N]

I hope you can understand :)

powerful computers now, not then

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