A block of mass 2.95708 kg lies on a friction-
less table, pulled by another mass 3.23123 kg
under the influence of Earth’s gravity.
The acceleration of gravity is 9.8 m/s2 .
What is the magnitude of the tension T of
the rope between the two masses?
Answer in units of N
EXPLAIN HOW AND WHY YOU SOLVED IT THAT WAY!!!
To find the magnitude of the tension force between the two masses, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
First, let's find the acceleration of the system. The net force on the system is the force applied by the hanging mass, T, minus the force due to the weight of the block.
The force applied by the hanging mass, T, can be calculated using its weight, which is the product of its mass and the acceleration due to gravity. Therefore, T = m1 * g, where m1 is the mass of the hanging mass and g is the acceleration due to gravity.
Next, we need to calculate the force due to the weight of the block. The weight of the block is the product of its mass and the acceleration due to gravity. Therefore, the force due to the weight of the block is m2 * g, where m2 is the mass of the block and g is the acceleration due to gravity.
Now, the net force acting on the system is T - m2 * g. According to Newton's second law, this net force should be equal to the total mass of the system multiplied by the acceleration of the system.
So, T - m2 * g = (m1 + m2) * a,
where m1 + m2 is the total mass of the system (m1 + m2 = 2.95708 kg + 3.23123 kg), and a is the acceleration of the system.
Since the block is on a frictionless table, the acceleration of the system is the same as the acceleration of the hanging mass.
Finally, we can solve for T by rearranging the equation:
T = (m1 + m2) * a + m2 * g
Plugging in the given values:
m1 = 3.23123 kg
m2 = 2.95708 kg
g = 9.8 m/s^2
We can calculate the tension T using the equation above.