A 90 N force is applied to a 50 kg object. If the same force is applied to a 70 kg object, how will the acceleration of the two objects compare?
Remember: [tex]F=m \cdot a[/tex]
A. The 70 kg object will have greater acceleration.
B. The 70 kg object will have smaller acceleration.
C. The 70 kg object will have the same acceleration.
Answer (2)
Calculate the acceleration of the 50 kg object: a 1 = 50 90 = 1.8 m/s 2 .
Calculate the acceleration of the 70 kg object: a 2 = 70 90 ≈ 1.29 m/s 2 .
Compare the accelerations: 1.29"> 1.8 > 1.29 .
The 70 kg object will have smaller acceleration: The 70 kg object will have smaller acceleration.
Explanation
Understanding the Problem We are given that a 90 N force is applied to a 50 kg object and then to a 70 kg object. We need to compare the accelerations of the two objects. We know that F = m \tims a , where F is the force, m is the mass, and a is the acceleration.
Calculating Acceleration of the First Object For the 50 kg object, we have F = 90 N and m 1 = 50 kg. Using the formula F = m 1 \tims a 1 , we can solve for the acceleration a 1 :
a 1 = m 1 F = 50 kg 90 N = 1.8 m/s 2
Calculating Acceleration of the Second Object For the 70 kg object, we have F = 90 N and m 2 = 70 kg. Using the formula F = m 2 \tims a 2 , we can solve for the acceleration a 2 :
a 2 = m 2 F = 70 kg 90 N ≈ 1.29 m/s 2
Comparing the Accelerations Comparing the accelerations, we have a 1 = 1.8 m/s 2 and a 2 ≈ 1.29 m/s 2 . Since 1.29"> 1.8 > 1.29 , the 50 kg object has a greater acceleration than the 70 kg object.
Final Answer Therefore, the 70 kg object will have smaller acceleration.
Examples
Imagine you're pushing two shopping carts, one full of groceries (50 kg) and another even more loaded (70 kg), with the same amount of force. The lighter cart will accelerate faster and be easier to maneuver, while the heavier cart will accelerate more slowly and require more effort to get moving. This principle applies in many real-world scenarios, such as understanding how different sized engines affect a car's acceleration or how varying loads impact a truck's ability to speed up.
The 70 kg object will have smaller acceleration compared to the 50 kg object when the same force is applied. The acceleration of the 50 kg object is approximately 1.8 m/s², while the 70 kg object has an acceleration of about 1.29 m/s². Thus, the answer is option B: The 70 kg object will have smaller acceleration.
;
