A 55kg person pushes on the floor with 800 N of force for 0.25 seconds. How high do they jump off the ground?
I know how to find acceleration but I can't find distance.
change in momentum = force * time
force up = 800 -55(9.81)
= 260 N net up force
so
momentum = m Vi = 260*.25 = 65
so
Vi = 65/55 = 1.18 m/s up
(1/2)mVi^2 = m g h
h = Vi^2/[2(9.81)] = .071 meters
= 7.1 cm
I haven't learned momentum yet, is there any way to do it with only Forces and F=ma as well as kinematics?
Thanks
Not really.
I bet you have heard the word "Impulse"
that is force * time
which is change of momentum
F = m a = m dv/dt
so
F dt = m dv = "impulse"
but m dv is change in m v
and m v is "momentum
therefore
F * time = change in momentum = impulse
To find the distance the person jumps off the ground, we can use the principles of kinematics. In this case, we know the initial velocity is zero since the person starts from rest on the ground. We also know the force exerted and the mass of the person. However, we need to find the acceleration first to determine the distance traveled.
To find the acceleration, we can use Newton's second law of motion, which states that force equals mass multiplied by acceleration (F = ma). Rearranging the equation, we can calculate the acceleration (a) as follows:
a = F / m
Using the given values, we have:
a = 800 N / 55 kg
Simplifying, we find:
a ≈ 14.55 m/s²
Now that we have the acceleration, we can determine the distance traveled using the equation of motion:
s = (1/2) * a * t^2
Where:
s is the distance traveled
a is the acceleration
t is the time
Plugging in the values, we have:
s = (1/2) * 14.55 m/s² * (0.25 s)^2
Simplifying further, we get:
s ≈ 0.45 m
Therefore, the person jumps approximately 0.45 meters off the ground.