How to find distance when given mass time and force
1 answer:
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a) 1.84 m
b) 1.55 m
Explanation:
a)
In this problem, the only force acting on Zak along the direction of motion (horizontal direction) is the force of friction, which is
where
is the coefficient of friction
m is Zak's mass
is the acceleration due to gravity
According to Newton's second law of motion, the net force acting on Zak is equal to the product between its mass (m) and its acceleration (a), so we have
Here the only force acting is the force of friction, so this is also the net force:
Therefore we can find Zak's acceleration:
Since Zak's motion is a uniformly accelerated motion, we can now use the following suvat equation:
where
v = 0 is the final velocity (he comes to a stop)
u = 3.00 m/s is the initial velocity
is the acceleration
s is the distance covered before stopping
Solving for s,
b)
In this second part, Zak gives a push to Greta.
We can find Greta's velocity after the push by using the work-energy theorem, which states that the work done on her is equal to her change in kinetic energy:
where
F = 125 N is the force applied by Zak
d = 1.00 m is the distance
is the force of friction, where
m = 20.0 kg is Greta's mass
v is Greta's velocity after the push
u = 0 is Greta's initial velocity
Solving for v, we find:
After that, Zak stops pushing, so Greta will slide and the only force acting on her will be the force of friction; so the acceleration will be:
And so using again the suvat equation, we can find the distance she slides after Zak's push ends:
where
v = 2.76 m/s is her initial velocity
v' = 0 when she stops
Solving for s,