Title : Force and Acceleration

Apparatus :

     Science Workshop Interface 750

        Motion Sensor ( PASCO Model CI 6742 )

        Force Sensor ( PASCO Model CI 6537 )

        Dynamics Cart

        Laboratory jack

        Runway

        Clamp-on pulley

        Mass and hang ( 1 set )

        String

        Metre rule

        Triple Beam Balance or Digital Balance

Objective :

Study the relationship between the applied force and acceleration of a constant mass

Theory :

Newton's second law of motion :

The rate of change of momentum of an object is proportional to the

resultant force which acts on the object and occurs in the direction of

the resultant force.

Or        F = m a     for a constant mass m

In practice, there is friction between the runway and the cart.

M a = F - f     where  F = applied force acting on the force sensor and cart

                                           f = friction

In order to eliminate the friction, the runway should be tilted in an angle θ such that  f = M g sin θ

Without the applied force, F, acting on the cart, the equation of motion of the cart is

            M a = M g sin θ - f = 0

              a = 0

The cart would move with constant velocity

With the constant applied force, F, acting on the cart, the equation of motion of the cart is

            M a = F 

The cart would accelerate with constant acceleration.

 The applied force, F, can be measured by a force sensor and the velocity of the cart can be measured by a motion sensor. The acceleration, a, of the cart can be obtained from the slope of v – t graph.

 By varying the mass on the hanger, a set of F and a can be obtained.

 The mass can be obtained from the slope of F - a graph.  

A force sensor measures the applied force in the range between – 50 Newtons and +50 Newtons.

A motion sensor emits ultrasonic pulses and detects pulses returned as echoes from the target. 

Procedure :

Basic setup :

1.  Connecting the Interface to the Computer

2.  Connecting the Motion Sensor and Force Sensor 

      to the Interface

3.  Calibrating the Motion Sensor

Setting up a friction-compensated runway

Varying the mass on the hanger

Recording the data with computer 

Measuring mass of the dynamics cart and the force sensor

Data Analysis :

1.    Determine Force and Acceleration Table

2.    Plot a graph of Net Force against acceleration

3.    Compare theoretical mass and actual mass

Discussion :

1.  What are the precautions of this experiment ?

2.  Why the curve does not pass through the origin ?

3.  Is the weight of the hanger equal to the applied force ?

4.  Account for the sources of error in this experiment.