Suppose a 65-kg boy and a 45-kg girl use a massless rope in a tug-of-war on an icy, resistance-free surface. If the acceleration of the girl toward the boy is 3.0 m/s2, find the magnitude of the acceleration of the boy toward the girl.
i want to know them
girl: 135 N
boy mass: 65 kg
135/65 = 2.0769 =
2.077 m/s^2
Tension of rope = T N
Mass of girl, m = 45 kg
Acceleration = 3.0 m/s²
T = ma = 135 N
Mass of boy, M = 65 kg
T = MA,
solve for acceleration A.
i want to know them too
To find the magnitude of the acceleration of the boy toward the girl, we can use Newton's second law of motion, which states:
F = m * a
where F is the force, m is the mass, and a is the acceleration.
In this case, the girl is experiencing a force towards the boy due to the tug-of-war. The magnitude of this force can be calculated as:
F = m * a
Taking the girl's mass as 45 kg and her acceleration as 3.0 m/s², we can calculate her force as:
F_girl = 45 kg * 3.0 m/s² = 135 N
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. Therefore, the boy will also experience a force of the same magnitude but in the opposite direction. So, the boy's force is:
F_boy = -135 N
Now, we can calculate the boy's acceleration using Newton's second law:
F_boy = m_boy * a_boy
Rearranging the equation, we get:
a_boy = F_boy / m_boy
Given the boy's mass as 65 kg, substituting the values, we can find the boy's acceleration:
a_boy = -135 N / 65 kg
Simplifying the expression gives us:
a_boy = -2.08 m/s²
Therefore, the magnitude of the acceleration of the boy toward the girl is 2.08 m/s².
-2.1
Mass of the boy is
m
1
=
65
k
g
Mass of the girl is
m
2
=
45
k
g
Acceleration of the girl towards the boy is:
a
1
=
3
m
/
s
2
For the force applied by the boy on the girl :
F
1
=
m
2
×
a
1
F
1
=
45
×
3
F
1
=
135
N
Now since the action and reaction pair will be same (
F
1
=
F
2
)now for the acceleration of the girl:
a
2
=
F
2
m
1
a
2
=
135
65
a
2
=
2.07
m
/
s
2
Thus, the acceleration of the girl towards the boy is
2.07
m
/
s
2
135 Newtons and 2.077 m/s2
no pb m8
The forces are the same
massman*aman=massgirl*agirl
solve for the man's acceleration