# The sum of the forces on an object is directly proportional to the mass of the…

The sum of the forces on an object is directly proportional to
the mass of the object and directly proportional to the
acceleration of the object. The second law is expressed by the
equation: (1) F=ma
If the mass is in kg and the acceleration in m/s2,
then the force is in Newtons.
In (1), F is the net applied force, m is the mass of the object
on which the force is applied, and a is the acceleration of the
object due to the applied net force.
A force will be applied to a cart of mass m1,
consisting of the mass of the cart plus added mass, by hanging
mass, m2, by a string that is attached to the cart over
a nearly frictionless pulley.
There is some friction in the pulley and between the cart and
track. Let Ffbe the frictional forces
that oppose the motion. Applying Newton’s second law to the cart
and the hanging mass and combining the two equations to eliminate
the tension in the string gives: (2) F2
= (m1 + m2)a + F
f

Where m1 + m2 is the total mass of the
system that includes the hanging mass and the mass of the
cart plus mass added to the cart. Notice that equation (2)
has the form of the equation of a straight line: y = Mx + b where M
is the slope of the line.
Question: compute the cart’s mass analytically from your
slope.
Data in picture

Thank you so much in advance!