Two objects are in contact on a frictionless surface. A horizontal force is applied to one object as shown in the figure below. Use m1 = 1.2 g, m2 = 254 g and F = 0.7 N to find the force between the two objects.
in the figure below...
To find the force between the two objects, we can use Newton's second law of motion.
Newton's second law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = ma
In this case, we are given the mass of one object (m1 = 1.2 g) and the applied force (F = 0.7 N). However, we need to find the force between the two objects, which means we need to find the acceleration of the system.
Since the objects are in contact on a frictionless surface, they will move together with the same acceleration.
Now, let's consider the second object (m2 = 254 g). Since the two objects are in contact, the force applied to the first object will also cause the second object to accelerate. This force is the force between the two objects, which we need to find.
Using Newton's second law, we can write the following equation for the second object:
F_between = m2 * a
Now, let's find the acceleration of the system. To do that, we need to use the total mass of the system, which is the sum of the masses of the two objects:
m_total = m1 + m2
m_total = 1.2 g + 254 g
m_total = 255.2 g
Now, we can rewrite the equation for the force between the two objects, using the total mass and the applied force:
F_between = m2 * a
F_between = (254 g) * a
F_between = (254 g) * (a / m_total)
F_between = (254 g) * (a / 255.2 g)
F_between = 0.995 g * a
Now, we can substitute the equation for force into Newton's second law to solve for the acceleration:
F = ma
0.7 N = (0.995 g) * a
a = (0.7 N) / (0.995 g)
Now, we can substitute the value of acceleration back into the equation for the force between the two objects to find the force:
F_between = 0.995 g * a
F_between = 0.995 g * [(0.7 N) / (0.995 g)]
F_between = 0.7 N
Therefore, the force between the two objects is 0.7 N.