# 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!