Uniformly Accelerated Motion

This activity observes the movement of a cart down an incline and investigates uniformly acceleration motion caused by gravity.

Theory

A cart placed on an inclined ramp starts to move straight down the ramp. This movement is due to the force of gravity acting on the cart to pull it down the incline and pulling it against the ramp. The distribution of these two forces depends on the inclination of the ramp. The acceleration of the cart is determined by the magnitude of the force that moves the cart. Movement represented by an acceleration value that does not change over time is called “uniformly accelerated motion.” The movement of the cart described above is uniformly accelerated motion. As shown below, the velocity of uniformly accelerated motion is proportional to time, and the distance traveled is proportional to the time squared. This means that if you observe the distance covered by the cart over a specific time, you can determine its acceleration.

F= ma =mg sinθ v = at

L =

1

at2

2

 

 

F(N)

: Force Acting on Cart in

 

 

Direction of the Ramp Surface

a(m/s2) : Cart Acceleration

m(kg)

: Cart Mass

g(m/s2) : Gravitational Acceleration

θ (°)

: Ramp Angle of Inclination

v(m/s)

: Cart Velocity

t(s)

: Cart Travel Time

L(m)

: Distance Traveled by Cart

Though actual gravitational acceleration depends on latitude and elevation, this activity can be

conducted using the gravitational constant 9.8m/s2.

2-1-1

English

Activity:tivity: SetupSetup

￿Equipment

Cart RampStandProtractor

Distance Measurement Setup (EA-200, graphic scientific calculator, data communication cable, optional EA-2*1)

￿Setting Up

uAffix the EA-2 to the arm of the stand.

uMeasure the incline of the ramp with the protractor, and fix the ramp at an angle of 15 degrees.

1 Stand

 

2 Ramp

 

3 Desk

 

4 EA-2 (SONIC)

 

5 Protractor

 

6 Ramp Angle:

 

15 degrees

 

7 Distance from EA-2 to

*1

end of ramp: 150cm

 

8 Ramp Width: 30cm

 

9 EA-200

 

 

 

uMeasure the mass of the cart, place it onto the ramp, and hold it in place with your hand.

1Desk

2Ramp

3EA-2 (SONIC)

4Cart Mass: m(kg)

5Distance Between Cart and EA-2: 60cm

6Protractor

7Ramp Angle: 15 degrees

8Hand

*1 When using the EA-200 in combination with the optional ‘‘Motion Sensor (EA-2) ”, be sure to power the EA-200 using its bundled AC adaptor (AD-A60024).

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