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Newton's Second Law: The Connection Between an Object's Acceleration and the Force Applied to it

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Author: Jerry Silver

The Idea

This classic experiment explores the connection between an object's acceleration and the force applied to it. This fundamental principle of physics was first formulated by Sir Isaac Newton in the famous second law of motion that bears his name. To measure acceleration, you use either the stopwatch or the motion sensor technique of measuring acceleration, which we used in previous experiments. The force will be provided courtesy of the Earth, in the form of the gravitation force on a mass hanging from a string.

What You Need

  • low-friction cart (or an air track and glider, if available)
  • spring scale
  • mass set (including 50 g, 100 g, 200 g)
  • tape
  • string
  • pulley (low mass and low friction is preferable)
  • clamp to attach the pulley to the table
  • table top (at least 1 meter in length)
  • stopwatch and meterstick or motion sensor

Method

  1. Determine the mass of the cart in grams. Divide by 1000 to get kilograms.
  2. Place a 100g (0.1kg) mass in the cart. Secure it with tape, if necessary.
  3. Set the cart at one end of the table, and attach the pulley to the other end.
  4. Attach the string to the cart, run it over the pulley, and tie a loop that extends a few inches below the edge of the table, in the other end, as shown in Figure 25-1.
  5. While holding the cart in position at the far end of the table, hang a mass on the loop on the other side of the string.
  6. Next, you release the cart and let the weight of the hanging mass pull the cart across the table. As you do this, you measure the acceleration of the cart using either of the previous methods:
    • Stopwatch: measure the time (in seconds) for the cart to be pulled a measured distance (in meters). The acceleration (in m/s2) is determined by a = 2d/t2, where d is the distance that the object is pulled across the table (in m) during time, t (in seconds).
    • Newton's second law. Forcing an object to accelerate.

    • Motion sensor: record the position of the cart as it is drawn across the table. Display the velocity versus time graph and determine the acceleration of the cart by finding the slope of that graph. This can be done either using the Slope tool from the DataStudio menu or more simply by obtaining the acceleration as the change in velocity divided by the change in time.
  7. Repeat this measurement, but make the following changes:
    • Vary the mass in the cart, but keep the applied force constant, as indicated in Figures 25-2 and 25-3.
    • Vary the applied force by adding or removing some of the hanging weight, but keep the mass in the cart constant, as shown in Figure 25-4.

Newton's second law. Forcing an object to accelerate.

Proving Newton's second law

Newton's second law, which states that F = ma, or as Newton originally put it, a = F/m.

  • m represents the entire mass of the system and includes the mass of the cart (mc), plus the mass in the cart (m1) plus the hanging mass (m2).
  • F is the applied force that pulls the cart and is given by the hanging mass, m2 (in kilograms, not in grams) times the gravitational acceleration (9.8 m/s2). (To get kilograms from grams, divide the number of grams by 1000.)
  • a is the acceleration (in m/s2) of the entire system, including the cart, its contents, and the hanging mass.

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