60.0 kg boy and a 40.0 kg girl are sitting in identical office chairs in a large warehouse. The coefficients of static and kinetic friction between the chairs and the horizontal floor are both 0.250. The boy puts his feet up against the girl’s chair and pushes it with a constant force of 375 N for 0.600 s. Determine how far apart the children come to rest.

Question

60.0 kg boy and a 40.0 kg girl are sitting in identical office chairs in a large warehouse. The coefficients of static and kinetic friction between the chairs and the horizontal floor are both 0.250. The boy puts his feet up against the girl’s chair and pushes it with a constant force of 375 N for 0.600 s. Determine how far apart the children come to rest.

4.

Answer 1

The objects are moving due to the law of the conservation of linear momentum

0 = m1•v1 + m2•v2,
F•Δt = m1•v1,
v1 = F•Δt/ m1 =375•0.6/60 =3.75 m/s
F•Δt = m2•v2,
v2 = F•Δt/m2= 375•0.6/40 =5.625 m/s

m1•(v1)^2/2 = k•m1•g•s1
s1 =3.75^2/1•0.25•9,8 = 2.87 m
m2•(v2)^2/2 = k•m2•g•s2
s2 =5.625^2/1•0.25•9,8 = 1.61 m

Answer 2

To determine how far apart the children come to rest, we need to use the concept of friction and Newton's laws of motion.

First, let's calculate the force of friction between the girl's chair and the floor. The formula for calculating the force of friction is:

Force of friction = coefficient of friction * normal force

The normal force is equal to the weight of the girl, which is the mass of the girl multiplied by the acceleration due to gravity (9.8 m/s^2). Therefore, the normal force on the girl's chair is:

Normal force = mass of the girl * acceleration due to gravity
Normal force = 40.0 kg * 9.8 m/s^2

Now, we can calculate the force of friction:

Force of friction = coefficient of static friction * normal force
Force of friction = 0.250 * (40.0 kg * 9.8 m/s^2)

Next, let's calculate the acceleration of the system using Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:

Net force = force of the boy - force of friction
Net force = 375 N - (0.250 * (40.0 kg * 9.8 m/s^2))

Now we can calculate the acceleration of the system:

Net force = (mass of the boy + mass of the girl) * acceleration
(375 N - (0.250 * (40.0 kg * 9.8 m/s^2))) = (60.0 kg + 40.0 kg) * acceleration

After calculating the acceleration, we can use the kinematic equation to find the distance the children come to rest. The equation is:

Distance = initial velocity * time + (1/2) * acceleration * time^2

Since the children start from rest, the initial velocity is 0 m/s. The time given is 0.600 s, and the acceleration is the value we calculated in the previous step.

Plug these values into the equation to find the distance the children come to rest.