Two objects are positioned and moving . m 1 = 7 kg ,m 2 =11 kg, and the coefficient of kinetic friction between object 1 and the tabletop is uk = 0.14. Find the acceleration of object 2(assuming up is the positive direction) as well as the tension in the string.
To find the acceleration of object 2 and the tension in the string, we can follow these steps:
Step 1: Find the net force acting on object 1.
Since object 1 is on a tabletop, the only horizontal force acting on it is the force of friction. The frictional force can be calculated using the equation:
f_friction = uk * normal force
where uk is the coefficient of kinetic friction and the normal force is the force exerted by the tabletop on object 1. In this case, the normal force is equal to the weight of object 1 (m1 * g, where g is the acceleration due to gravity).
Step 2: Find the acceleration of object 1.
The net force acting on object 1 can be calculated using Newton's second law:
net force = m1 * a1
where m1 is the mass of object 1 and a1 is its acceleration. Rearranging this equation, we get:
a1 = net force / m1
Step 3: Find the tension in the string.
Since object 1 and object 2 are connected by a string, they experience the same tension. The net force acting on object 2 is equal to the tension pulling it up, minus the force of gravity:
net force = T - m2 * g
where T is the tension in the string and m2 is the mass of object 2.
Step 4: Find the acceleration of object 2.
Using Newton's second law again, the net force acting on object 2 can be calculated:
net force = m2 * a2
where a2 is the acceleration of object 2. Rearranging this equation, we get:
a2 = net force / m2
Now, let's plug in the values given in the question.
m1 = 7 kg (mass of object 1)
m2 = 11 kg (mass of object 2)
uk = 0.14 (coefficient of kinetic friction)
Step 1:
frictional force = uk * normal force
normal force = m1 * g
Step 2:
a1 = net force / m1
Step 3:
net force = T - m2 * g
Step 4:
a2 = net force / m2
By solving these equations, we can find the acceleration of object 2 (a2) and the tension in the string (T).