Free fall and Newtons second law

In summary, a person jumps from a 4.4 m high roof and bends their knees to decelerate over 0.70 m. The mass of their torso is 40 kg. The velocity just before their feet strike the ground is 9.2865 m/s. The average force exerted on their torso by their legs during deceleration is 2464 Newtons, but this only accounts for the net upward force and does not take into account the downward gravitational force.
  • #1
alexoftennis
4
0

Homework Statement



A person jumps from the roof of a house 4.4 m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. The mass of his torso (excluding legs) is 40 kg.

(a) Find his velocity just before his feet strike the ground. ( I found as 9.2865)

(b) Find the average force exerted on his torso by his legs during deceleration. (I found as 2464 BUT THIS IS WRONG. I NEED YOUR HELP TO GET THIS. Thanks!)

Homework Equations





The Attempt at a Solution



(v final) ^2- (v initial)^2 = 2as
a = 9.8 m/s
s=4.4
v initial = 0
solve for v final
v final = 9.2865 m/s

same equation is used in reverse
v final = 0
v initial = 9.2865 m/s
s = 0.70 m this time
solve for a
a = 61.60 m/s

F = ma m is 40kg
F = 40*61.60 = 2464 Newtons.
 
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  • #2
2464 N is the net upward force exerted on his torso, not the force exerted on his torso by his legs - his torso still experiences a downward gravitational force.
 

Related to Free fall and Newtons second law

1. What is free fall?

Free fall is the motion of an object when it is only influenced by the force of gravity. This means that there are no other forces, such as air resistance, acting on the object.

2. What is Newton's second law?

Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This can be represented by the equation F=ma, where F is the net force, m is the mass, and a is the acceleration of the object.

3. How do free fall and Newton's second law relate?

In free fall, an object is accelerating due to the force of gravity. This acceleration can be calculated using Newton's second law, where the net force is equal to the force of gravity (weight) and the mass of the object. This can be written as F=mg, where g is the acceleration due to gravity (9.8 m/s^2 on Earth).

4. Does the mass of an object affect its acceleration during free fall?

According to Newton's second law, the mass of an object does affect its acceleration during free fall. The greater the mass of the object, the greater the force of gravity needed to accelerate it at a certain rate. This means that objects with larger masses will have a slower acceleration during free fall compared to objects with smaller masses.

5. What is terminal velocity in relation to free fall and Newton's second law?

Terminal velocity is the constant speed that an object reaches when the force of gravity is balanced by the force of air resistance. This occurs during free fall when an object can no longer accelerate due to the increasing air resistance as it falls. This means that the object will continue to fall at a constant speed until it reaches the ground, as predicted by Newton's second law.

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