The figure below shows an object of mass M = 1,276 g. It is free to move along a horizontal, frictionless surface. This object is further connected to a second object with a mass of m = 1,362 g by means of a massless string that extends around a massless, frictionless pulley. Find the tension of the massless string.
The figure:
M is placed on a table/surface where m is hanging down with the string attaching it to M.
Thank you.
so m is pulling M.
force equation:\
mg=(M+m)a solve for a.
Then, tension = force pulling M or M*a
from the FBDs wouldnt u get
for M:
Fy = N-WM=Ma
Fx=T=Ma
for m:
Fy= T-Wm=ma
Fx= T-W=ma
then solve for a in M of Fx
and sub a into m of Fx to get T?
Sorry i see the mistake I made
for m the acceleration would be negative since its moving down
To determine the tension in the string, we need to analyze the forces acting on both objects connected by the string.
First, let's consider the object with mass M on the table. The only force acting on it is its weight, which can be calculated using the formula:
Weight = mass * acceleration due to gravity
The weight of the object with mass M is given by:
Weight of M = M * g,
where g is the acceleration due to gravity.
Next, let's consider the object with mass m hanging from the string. The forces acting on it are its weight, which is directed downward, and the tension in the string, which is directed upward.
Since the objects are connected by a string passing over a pulley, the tension in the string will be the same for both objects.
By applying Newton's second law (F = ma) to the object with mass m, we can write:
Tension - Weight of m = m * a,
where a is the acceleration of the system.
Since the system is assumed to be in equilibrium (not accelerating), the acceleration (a) is zero. Therefore:
Tension - Weight of m = 0,
Tension = Weight of m.
Now, we can substitute the weight of m using the formula:
Weight of m = m * g.
Substituting the given values for m and g:
Weight of m = 1,362 g * 9.8 m/s^2 = 13,369.6 g * m/s^2.
Converting grams to kilograms (since we're using the standard metric unit for force, which is Newtons):
Weight of m = 13.3696 kg * 9.8 m/s^2 = 130.9888 N.
Therefore, the tension in the massless string is equal to 130.9888 Newtons.