Question

Newton's Second Law of Motion

Nash is investigating the relationship between the net force on an object and the acceleration of the object. He uses a spring scale to measure the force that is used to pull a cart along a track. He is able to change the mass of the cart by stacking steel plates on top of the cart. Nash sets up two photogates along the track. The photogates are used to accurately record the exact time the cart passes in front of them. This information can be used to calculate the average speed of the cart at and between the two photogates. The setup of the experiment is shown below. 

test force (n) mass (kg) acceleration (m/s^2)
1 1.0 1.2 0.83
2 1.0 1.6 0.63
3 1.0 1.2 ?
4 1.0 1.8 1.1

Constructed Response Question

Nash collected the data shown in the table using the experimental setup.



A. Calculate the acceleration of the cart during Test 3 as described in the table. Show all your work and provide units in your answer.

B. Make a claim about the relationship between the net force on an object and the acceleration of the object that is supported by data in the table.

Answer 1

A. Use Newton’s 2nd law: F = m a, so a = F / m.
For Test 3: a = 1.0 N / 1.2 kg = 0.8333… m/s^2 ≈ 0.83 m/s^2.

B. Claim supported by the data: For a given net force, acceleration is inversely proportional to mass (a = F/m). Evidence: Tests 1 and 2 use the same force (1.0 N); when mass increases from 1.2 kg to 1.6 kg, acceleration falls from 0.83 m/s^2 to 0.63 m/s^2. (Also the product m·a ≈ 1.0 N in those trials, consistent with F = m a.)