An object of mass m1 = 4.10 kg placed on a frictionless, horizontal table is connected to a string that passes over a pulley and then is fastened to a hanging object of mass m2 = 6.70 kg as shown in the figure
-> Find the magnitude of the acceleration of the objects.
(m/s2)
-> Find the tension in the string.
(N)
tension = T newtons
bottom block:
6.7 g - T = 6.7 a
top block on table:
T = 4.1 a
so
6.7(9.81) - 4.1 a = 6.7 a
etc
To find the magnitude of the acceleration of the objects, we can use Newton's second law of motion. According to this law, the net force acting on an object is equal to the product of its mass and acceleration. We can set up an equation for each object and then solve for the acceleration.
For the object of mass m1 on the table:
The only force acting on this object is the tension in the string, directed horizontally. Therefore, the net force on this object is equal to the tension.
m1 * a = Tension
For the hanging object of mass m2:
The weight of the object is acting vertically downwards, and the tension in the string is acting upwards. Therefore, the net force on this object is the difference between the tension and the weight.
m2 * g - Tension = m2 * a
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
We can now solve these two equations simultaneously to find the magnitude of the acceleration and the tension in the string.
Let's substitute known values into the equations:
m1 = 4.10 kg
m2 = 6.70 kg
g = 9.8 m/s^2
For the object on the table:
4.10 kg * a = Tension (Equation 1)
For the hanging object:
6.70 kg * 9.8 m/s^2 - Tension = 6.70 kg * a (Equation 2)
Now we can solve these two equations simultaneously to find the values of acceleration and tension.