A 6.0-kg object undergoes an acceleration of 2.6 m/s2.
(a) What is the magnitude of the resultant force acting on it?
N
(b) If this same force is applied to a 12.0-kg object, what acceleration is produced?
m/s2
A bag of sugar weighs 2.00 lb on Earth. What would it weigh in newtons on the Moon, where the free-fall acceleration is one-sixth that on Earth?
N
Repeat for Jupiter, where g is 2.64 times that on Earth.
N
Find the mass of the bag of sugar in kilograms at each of the three locations.
Earth kg
Moon kg
Jupiter kg
For the last part, mass stays the same regardless of location. Weight changes, mass stays the same.
To find the magnitude of the resultant force acting on the 6.0-kg object, you can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration. Here's how you can calculate it:
(a) To find the magnitude of the resultant force, use the formula:
Force = mass × acceleration
Given:
Mass of the object (m) = 6.0 kg
Acceleration (a) = 2.6 m/s^2
Substituting the values into the formula:
Force = 6.0 kg × 2.6 m/s^2
Calculating this, you find:
Force = 15.6 N
Therefore, the magnitude of the resultant force acting on the 6.0-kg object is 15.6 Newtons.
(b) Now, let's determine the acceleration produced when the same force is applied to a 12.0-kg object.
Using the same formula as before:
Force = mass × acceleration
Now we have:
Mass of the object (m) = 12.0 kg
Force (F) = 15.6 N (from part a)
Rearranging the formula to solve for acceleration:
acceleration = Force / mass
Substituting the values:
acceleration = 15.6 N / 12.0 kg
Calculating this, you find:
acceleration ≈ 1.3 m/s^2
Therefore, when the same force is applied to a 12.0-kg object, it would produce an acceleration of approximately 1.3 m/s^2.