An object of mass M = 1,114 g is free to move along a horizontal, frictionless surface. This object is further connected to a second object with a mass of m = 811 g by means of a massless string that extends around a massless, frictionless pulley. Find the tension of the massless string.
pulling force mg
acceleration= mg/(M+m)
tension= ma
revise that to tension=Ma, it is the mass on the table * acceleration
Thank you
To find the tension in the massless string, we can use Newton's second law and the fact that there is no friction or acceleration in the system.
Let's assume that the first object with mass M is on the left side and the second object with mass m is on the right side.
First, let's establish the equations of motion for each object:
For the first object (mass M):
The only force acting on the first object is the tension in the string pulling it to the right. Therefore, we can write the equation of motion as:
T = M * a
Where T is the tension in the string and a is the acceleration of the system.
For the second object (mass m):
The only force acting on the second object is the tension in the string pulling it to the left. Therefore, we can write the equation of motion as:
T = m * g - m * a
Where T is the tension in the string, m * g is the weight of the second object, and a is the acceleration of the system.
Now, since the two objects are connected by a string, they must have the same acceleration:
a = -a (the negative sign indicates opposite direction)
Substituting this value of a in the equation for the second object, we get:
T = m * g + m * a
Now, let's combine the equations for the first and second objects:
M * a = m * g + m * a
Simplifying this equation, we find:
(M - m) * a = m * g
a = (m * g) / (M - m)
Now, substituting this value of a back into the equation for the tension in the string on the first object, we have:
T = M * a
T = M * (m * g) / (M - m)
Substituting the given values M = 1114 g and m = 811 g, and assuming the acceleration due to gravity g = 9.8 m/s^2, we can calculate the tension in the string:
T = (1114 g) * (811 g) / (1114 g - 811 g)
T = 901,954 g^2 / 303 g
T ≈ 2976 g
Therefore, the tension in the massless string is approximately 2976 g (grams).
Note: Remember to convert the mass to kilograms if necessary in order to use SI units.