Help - Block on Springs

The applet simulates the forces acting on a vertically moving block. The block is supported by springs that in turn are resting on a platform (Table). The table can move upward or downward.

Click on a number to view the explanation of the corresponding item.

  1. Basic Control Buttons

    2. There are three basic control buttons. They are, from left to right:

    Rewind Rewind. Resets the simulation to the initial position with the previously chosen initial values.

    After clicking Rewind, click Play to restart the motion.

    Play Play/Pause. Starts the motion.

    After Play has been clicked, the button will change into the Pause button Pause. Clicking Pause will freeze the motion. To resume the motion, click Play once more.

    Reset Reset. Resets the applet to its default setting.

    Adjustments in the initial position and velocity can only be made after first clicking REWIND or RESET. However, the acceleration of the block-springs-table system can be adjusted during the motion.

    Back to Top

  2. Reference Frames Mode Buttons

    3. By selecting one of the two radio buttons you can choose either

    The Lab Frame is an inertial frame, the Object Frame a non-inertial frame (if the acceleration is non-zero).

    In the non-inertial Object Frame, there is a fictitious force in addition to the two real forces (normal and gravitational) that exist equally in both frames. This fictitious force is displayed as a black vector in the free-body diagram when the Object Frame mode is selected. Also, when in this mode, the acceleration vector displayed by the applet is not the acceleration of the block in this frame, which is zero, but the acceleration vector A of the Object Frame relative to the Lab Frame.

    Back to Top

  3. Sliders

    4. Two Sliders

    There are two sliders for adjusting the following variables. Both variables are scalar components relative to a y-axis that points vertically upward.

    Clicking on a slider to the left or right of the slider tab allows fine adjustment of the slider setting.

    Clicking on the Input Dialog button Input Dialog Button of a slider opens a dialog for entering an exact value for the slider setting. The dialog for the Acceleration slider is illustrated below. The range in which values can be entered, from -4.00 m/s2 to 4.00 m/s2 in this case, is indicated above the data entry field.

    Input Dialog Field

    The Acceleration slider remains active during the motion and can be used to change the acceleration while the motion is in progress. While the slider is not being adjusted, the acceleration is constant.

    If the applet is in the Lab Frame mode, the acceleration set by the slider is the (y-component of the) acceleration vector a of the system (table-springs-block) relative to the Lab frame. If the applet is in the Object Frame mode, the acceleration set by the slider is the (y-component of the) acceleration vector A of the Object Frame relative to the Lab Frame.

    The Velocity slider can be used to set the (y-component of the) initial velocity of the system relative to the Lab frame. The slider is inactive during the motion so that its setting cannot be changed during the motion or when the motion is paused. Nevertheless, it displays the instantaneous velocity of the system relative to the Lab frame at all times. It does this both in the Lab Frame or Object Frame modes.

    Comment. Since the system is always at rest relative to the Object frame, by definition of the Object frame, the velocity of the system relative to the Lab frame is equal to the velocity of the Object frame relative to the Lab frame.

    Back to Top

  4. Speedometer

    5. Speedometer

    The red needle displays the system's speed relative to the Lab Frame, or the speed of the Object Frame relative to the Lab frame, depending on which frame is selected.

    Comment. The values shown by the speedometer are always positive or zero, because of the definition of speed. In constrast, both positive and negative values are shown by the Velocity slider because the y-component of the velocity can be either positive or negative.

    Back to Top

  5. Acceleration Vector AccelerationVector

    6. The acceleration vector set by the Acceleration slider is represented by an orange arrow near the right edge of the applet window. The vector is labeled vector a or vector A depending on whether the applet is in the Lab Frame or Object Frame mode, respectively.

    When the acceleration is zero, the acceleration is represented by an orange dot, labeled vector a = 0 or vector A = 0, depending on the mode.

    The mouse cursor changes from a pointing arrow to a pointing hand when placed over the tip of the acceleration vector. At this time, you can change the acceleration by clicking and dragging the tip of the vector. Dragging the vector provides an alternate means of setting the acceleration. (See Point 3 above for setting the acceleration by means of a slider.) The acceleration vector can be adjusted during the motion, either by dragging the arrow or by adjusting the acceleration slider.

    Back to Top

  6. Free-Body Diagram For The Block

    7. In the Lab Frame mode, the free-body diagram for the block (left image) shows the two (real) forces acting on the block: the gravitational force of magnitude W exerted by the earth on the block and the normal force of magnitude N exerted by the springs on the block. The gravitational force stays the same no matter how the system is adjusted, but the normal force depends on the block's acceleration, but not on its velocity.

    In the Object Frame mode, the free-body diagram (middle image) shows the fictitious force (in black) that exists only in this non-inertial frame, in addition to the same two real forces as in the Lab Frame. The vector sum of these three forces, including the fictitious force, is equal to zero, because the system's acceleration vector a' relative to the Object Frame is equal to zero.

    Back to Top

  7. The System

    8. Initially or upon Reset or Rewind, the system's initial position can be adjusted upward or downward by clicking on either the table, springs, or block with the mouse and dragging.

    Back to Top

  8. Time

    9. In the top left corner of the applet window, the time elapsed since the beginning of the motion is displayed in seconds.

Back to Top