Which describes how the same force affects a small mass and a large mass
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Newton's second law allows us to find the results for the displacement and work on box 1 are:
1) The displacement is
2) The work is
1) Newton's second law says that force is directly proportional to the mass and acceleration of bodies.
F = ma
Where the bold letters indicate vectors, F is the force, m the mass and the acceleration of the bodies
The reference system is a coordinate system with respect to which the decompositions of the forces are carried out and all the measurements are made, in this case we take a system where the x axis is horizontal, the y axis is vertical and the zero of the system is located at soil
In the attached we can see a free body diagram of the system where the external forces are indicated, let's apply Newton's second law to body 1
body 1
x-axis
-T = m₁ a
body 2
y-axis
T - W₂ = m₂ a
W₂ = m₂ g
let's solve the system
- m₂ g = (m₁ + m₂) a
a = - m2 / m1 + m2 g
Kinematics studies the movement of bodies, let's use the expression
v² = - 2 a x
When the body stops the velocity is zero
x =
We substitute
Since the two boxes are connected by a rope, they both travel the same distance
2) They ask for Tension work on box 1
Work is defined by the scalar product of force and displacement
W = F. d
Where the bold letters indicate vectors, W is the work that is a scalar, F the force and d the displacement
We can write this expression by developing the dot product
W = F d cos θ
Where θ is the angle between force and displacement.
In this case the force is the tension of the rope, from the attached graph we see that the force is directed to the right and the displacement is to the left, therefore the angle is 180º and the cos 180 is equal to -1
We look for the tension from Newton's second law for box 1
T = - m₁ a
Let's substitute
T =
T =
We calculate the work
W = - ½ m₁ v₀²
In conclusion using Newton's second law we can find the results for the displacement and work on box 1 are:
1) The displacement is x=
2) The work is W = - ½ m₁ v₀²
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