 # The Relationship Involving Acceleration, Net Force, and Mass

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The Relationship Involving Acceleration, Net Force, and Mass

Giho Park

Purpose

The purpose of this lab investigation is to observe the relationship among the net force, mass, and acceleration of an object.

Hypothesis/Prediction

Part A

If the net force increases with a constant mass,

then the acceleration would increase,

because the force would push the object to increase the velocity.

Part B

If the mass of the cart increases with a constant net force,

then the acceleration would increase

because the greater inertia of the object would cause the acceleration to decrease.

Materials

ticker timer, ticker tape, cart, masking tape, one 2-m board, marker, ruler, spring scale, three 100-g masses, two 1.0-kg masses, string,

Procedure

Part A: Acceleration and Net Force

1. Verify that the equipment you intend to use is functioning properly.

2. Measure the mass of the cart and record it in the observation table.

3. Set up the apparatus so that the least net force will act on the cart. Allow the motion to occur and obtain the data required to find the acceleration &#945;1.

4. Repeat the procedure with an increased net force. For example, you can transfer one of the 100-g masses from the cart to the string hanging over the pulley. This allows the mass of the system to remain constant. Determine the data for &#945;2.

5. Repeat the procedure with the highest net force to determine the data for &#945;3.

Part B: Acceleration and Mass

6. Use the data for &#945;3 as the first set of data in this part of the experiment. Call the acceleration &#945;4.

7. Keep the net force constant at the highest value, but add a 1.0-kg mass to the cart. Perform the trial to obtain the data for &#945;5.

8. Add another 1.0-kg mass. Repeat the step to determine the data for &#945;6.

Observations

Trial Total mass of system (kg) Net force

(N [fwd]) Time (s) Displacement

(m [fwd]) Acceleration (m/s2 [fwd]) Ratio of net force to mass (N/kg)

&#945;1 1.1 1.0 51/60 0.2896 0.8017 0.91

&#945;2 1.1 2.0 35/60 0.2938 1.727 1.8

&#945;3 1.1 3.0 28/60 0.2929 2.690 2.7

&#945;4 1.1 3.0 28/60 0.2929 2.690 2.7

&#945;5 2.1 3.0 38/60 0.2992 1.492 1.4

&#945;6 3.1 3.0 42/60 0.2759 1.126 0.97

Analysis

(c) Trial &#945;1 : 1.0N/1.1kg = 0.9090909…. &#8756; The ratio of the net force to the total mass is 0.9N/kg.

Trial &#945;2 : 2.0N/1.1kg = 1.8181818…. &#8756; The ratio of the net force to the total mass is 1.8N/kg.

Trial &#945;3 : 3.0N/1.1kg = 2.7272727…. &#8756; The ratio of the net force to the total mass is 2.7N/kg.

Trial &#945;5 : 3.0N/2.1kg = 1.4285714…. &#8756; The ratio of the net force to the total mass is 1.4N/kg.

Trial &#945;6 : 3.0N/3.1kg = 0.9677419…. &#8756; The ratio of the net force to the total mass is 1.0N/kg.

(d)

m = (y2-y1)/x2-x1)

= 3.00-0.00

/3.30-0.20

= 3.00/3.10

= 0.96774

&#8756; = 0.97

The graph has a constant slope, which indicates that the net force is directly proportional to the acceleration.

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