Respuesta :
10 m/s² to the left.
Further explanation
Given:
- The mass of a stuffed bear = 200 grams = 0.2 kg.
- The mass of a boy = 25 kg.
- The mass of a girl = 20 kg.
- A boy pulls to the right with a 15 N force.
- A girl pulls to the left with a 17 N force.
Question:
What the acceleration of the bear is?
This is the case for implementing Newton's second law, i.e., 'the resultant force is proportional to the acceleration'. If we also use SI units then 'the resultant force is equal to the product of the mass and the acceleration'.
[tex]\boxed{\boxed{ \ F_{net} = m \cdot a \ }}[/tex]
- The net force, i.e., [tex]F_{net}[/tex] is the resultant of all forces acting on an object, measured in newtons (kgm/s²).
- The mass measured is kilograms.
- The acceleration measured in m/s².
Let's calculate the net force.
Referring to the horizontal axis marked a positive to the right, then
[tex]\boxed{ \ F_{net} = 15 - 17 = - 2 \ N \ }[/tex]
A negative sign indicates that the bear is moving to the left.
We continue to calculate the bear's acceleration. Remember, the mass that is applied is the mass of the bear that is accelerating.
[tex]\boxed{ \ F_{net} = m \cdot a \rightarrow a = \frac{F_{net}}{m_{bear}} \ }[/tex]
[tex]\boxed{ \ a = \frac{2 \ kg.ms^{-2}}{0.2 \ ms^{-2}} \ }[/tex]
Thus, the magnitude and direction of the acceleration is [tex]\boxed{\boxed{ \ a = 10 \ m/s^2 \ to \ the \ left \ }}[/tex]
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Keywords: two children, a 200 g stuffed bear, the 25 kg boy pulls to the right, a 15 n force, the 20 kg girl, left, a 17 n, what the acceleration, newton's second law, the magnitude and direction
The acceleration of the bear is [tex]\boxed{10{\text{ }}{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {{{\text{s}}^2}}}} \right. \kern-\nulldelimiterspace} {{{\text{s}}^2}}}}[/tex] and its direction of motion is towards left side.
Further explanation:
The net force acting on the bear is equal to the difference between force applied by the girl on the bear and force applied by boy on the bear.
Given:
The mass of the bear is [tex]200{\text{ g}}[/tex].
The force applied by the boy on the bear, towards right side, is [tex]15{\text{ N}}[/tex].
The force applied by the girl on the bear, towards left side, is [tex]17{\text{ N}}[/tex].
The mass of the boy is [tex]25{\text{ kg}}[/tex].
The mass of the girl is [tex]20{\text{ kg}}[/tex].
Formula and concept used:
From the Newton’s law of motion,
[tex]\sum F=ma[/tex]
Here, [tex]\sum F[/tex] is the net force acting on the object, [tex]m[/tex] is the mass of object and [tex]a[/tex] is the acceleration.
The weight of the boy and the girl will not affect the net force applied by them on the bear.
The net force applied on the bear is equal to the difference between force applied by the girl and force applied by the boy because the forces applied by the boy and girl are parallel to each other but opposite in the direction.
Therefore, from the vector law, the resultant of the parallel vectors acting opposite in direction is equal to the difference between their magnitudes. The direction of the resultant can be specified as the direction of the vector on larger magnitude.
The expression for the net force on the bear is:
[tex]\boxed{ma={F_g} - {F_b}}[/tex] …… (1)
Here, [tex]{F_g}[/tex] is the force applied by the girl, [tex]{F_b}[/tex] is the force applied by the boy, [tex]m[/tex] is the mass of bear and [tex]a[/tex] is the acceleration of the bear.
Thus, the acceleration of the bear is [tex]\boxed{10{\text{ }}{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {{{\text{s}}^2}}}} \right. \kern-\nulldelimiterspace} {{{\text{s}}^2}}}}[/tex] and its direction of motion is towards left side.
Calculation:
Substitute the value of [tex]{F_g}[/tex], [tex]{F_b}[/tex] and [tex]m[/tex] in equation (1).
[tex]\begin{aligned}\frac{{200}}{{1000}}a&=17 - 15 \\0.2a&=2 \\a&=10{\text{ }}{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {{{\text{s}}^2}}}} \right. \kern-\nulldelimiterspace} {{{\text{s}}^2}}} \\ \end{aligned}[/tex]
Learn more:
1. Acceleration of body by considering friction: https://brainly.com/question/7031524
2. The energy density stored in the capacitor: https://brainly.com/question/9617400
3. The motion of projectile: https://brainly.com/question/161035
Answer detail:
Grade: College
Subject: Physics
Chapter: Dynamics of motion
Keywords:
Two children fighting, force on the bear, acceleration, newton's law, boy, girl, pulling bear towards left, 10m/s2, 10m/s^2, 10.0m/s2 , 10.0m/s^2, mass, net force, weight, magnitude and direction.
