Two rubber bands pulling on an object cause it to accelerate at 1.6 m/s2.
(a) What will be the object's acceleration if it is pulled by six rubber bands?
(b) What will be the acceleration of six of these objects glued together if they are pulled by two rubber bands?
To find the acceleration in both scenarios, we can use Newton's second law of motion, which states that the force on an object is equal to the mass of the object multiplied by its acceleration.
Let's start with part (a):
(a) What will be the object's acceleration if it is pulled by six rubber bands?
Given:
Acceleration when pulled by 2 rubber bands = 1.6 m/s²
To calculate the acceleration when pulled by six rubber bands, we need to consider that the acceleration is directly proportional to the force applied. So, the acceleration will increase in proportion to the number of rubber bands.
We can use the following equation:
Acceleration ∝ Force
Since we know that the force applied is directly proportional to the number of rubber bands, we can write:
Force ∝ Number of rubber bands
Using this relation, we can say:
Acceleration ∝ Number of rubber bands
To find the new acceleration, we need to multiply the original acceleration by the number of rubber bands:
New acceleration = Original acceleration × Number of rubber bands
Plugging in the values:
New acceleration = 1.6 m/s² × 6
Therefore, the object's acceleration when pulled by six rubber bands will be 9.6 m/s².
Now let's move on to part (b):
(b) What will be the acceleration of six of these objects glued together if they are pulled by two rubber bands?
Given:
Acceleration when pulled by 2 rubber bands = 1.6 m/s²
To find the acceleration of six objects glued together when pulled by two rubber bands, we need to consider that the force applied will be multiplied by the number of objects.
Since the force applied is directly proportional to the number of objects, we can write:
Force ∝ Number of objects
Using this relation, we can say:
Acceleration ∝ Number of objects
To find the new acceleration, we need to multiply the original acceleration by the number of objects:
New acceleration = Original acceleration × Number of objects
Plugging in the values:
New acceleration = 1.6 m/s² × 6
Therefore, the acceleration of six of these objects glued together, if they are pulled by two rubber bands, will also be 9.6 m/s².