An object with mass m1=5.00 kg rests on a frictionless horizontal table and is connected to a cable that passes over a pulley and is then fastened to a hanging object with mass m2= 10.0 kg. Find the acceleration of each object and the tension in the cable.
the pulling force is m2*g
the masses being pulled is m1+m2
F=ma
a= F/m= m2*g/(m1+m2)
tension in the cable: Tension=m1*a
TANGINA MO
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Why did the table go to therapy? It had a heavy weight on its shoulders!
Now, let's get down to business. According to Newton's second law, we can analyze the forces acting on each object individually and then use the principle of the conservation of mass to relate their accelerations.
Let's start with the object on the table, m1. Since there is no friction, the only force acting on it is the tension in the cable. Let's call the acceleration of m1 "a1" and the tension in the cable "T".
For m1:
T - m1 * g = m1 * a1
Next, let's move to the hanging object, m2. The force of gravity is acting downwards, and the tension in the cable is acting upwards. Let's denote the acceleration of m2 as "a2".
For m2:
m2 * g - T = m2 * a2
Since the two objects are connected by the same cable, the accelerations of both objects are the same, i.e., a1 = a2 = a.
To find the values of a and T, we can solve these two equations simultaneously. Plugging in the given values for m1 (5.00 kg) and m2 (10.0 kg), and assuming g (acceleration due to gravity) is approximately 9.8 m/s², we can crack some math jokes and calculate the acceleration and tension.
To find the acceleration of each object and the tension in the cable, we can use Newton's second law of motion, F = ma, where F is the net force acting on the object, m is the mass of the object, and a is the acceleration.
Let's consider the object with mass m1. Since there is no friction and the table is horizontal, the only force acting on this object is the tension in the cable. Therefore, we can write:
Tension = m1 * a1
Now let's consider the hanging object with mass m2. The force of gravity acting on this object can be written as:
Force of gravity = m2 * g
Since the hanging object is being pulled upward by the tension in the cable, the net force acting on it is the difference between the force of gravity and the tension:
Net force = Force of gravity - Tension
Using Newton's second law, we have:
m2 * a2 = Net force
Now, since the two masses are connected and move together, their acceleration must be the same. Therefore, we can write:
a1 = a2 = a
Now let's solve the equations based on the given information:
For the object with mass m1:
Tension = m1 * a
For the hanging object with mass m2:
m2 * a = m2 * g - Tension
Substituting the value of Tension from the equation of the object with mass m1 into the equation of the hanging object, we get:
m2 * a = m2 * g - m1 * a
Simplifying this equation, we have:
m2 * a + m1 * a = m2 * g
Combining the like terms, we get:
(a * m2 + a * m1) = m2 * g
a * (m2 + m1) = m2 * g
Finally, we can find the acceleration:
a = (m2 * g) / (m1 + m2)
Once we have the acceleration, we can substitute it back into either of the equations to find the tension in the cable:
Tension = m1 * a
Now, let's calculate the values based on the given masses:
m1 = 5.00 kg
m2 = 10.0 kg
g = acceleration due to gravity = 9.8 m/s^2
a = (10.0 kg * 9.8 m/s^2) / (5.00 kg + 10.0 kg)
a = 4.9 m/s^2
Tension = 5.00 kg * 4.9 m/s^2
Tension = 24.5 N
Therefore, the acceleration of each object is 4.9 m/s^2, and the tension in the cable is 24.5 N.