Lab#12 Conservation Of Energy--Mass Spring System

Purpose：
    Verify the conservation of energy by using a mass- spring system. We will looking at the energy in a vertical- oscillating mass- spring system, where the spring has a non-negligible mass.

Set up:
      we have a hang in the certain distance above the motion sensor which place on the floor. The Distance H could be measure by a meter stick. We set the distance from the bottom of the un-stretch spring is h. Note that this can not be compressed. We could weight the mass of the spring M-spring and the hanging mass M- hanging. Placing a hanging mass at the bottom end of the spring, and a force sensor at the top end of the spring.

Lab#12 Conservation Of Energy--Mass Spring System

Purpose：
 Verify the conservation of energy by using a mass- spring system. We will looking at the energy in a vertical- oscillating mass- spring system, where the spring has a non-negligible mass.

Set up:
      we have a hang in the certain distance above the motion sensor which place on the floor. The Distance H could be measure by a meter stick. We set the distance from the bottom of the un-stretch spring is h. Note that this can not be compressed. We could weight the mass of the spring M-spring and the hanging mass M- hanging. Placing a hanging mass at the bottom end of the spring, and a force sensor at the top end of the spring.

Lab#13 Magnetic Potential Energy Lab

Lab: Magnetic Potential Energy Lab

Name: Xuhong Zhao

Partners: Amber  .

Date: 13th April 2015

Purpose:

     Verify that conservation of energy applies to this system.

Set up:

    Set up a frictionless cart with a strong magnet on one end approaches a fixed magnet of the same polarity, Make sure the air track is balanced.   When the cart is at the position of closet approach to the fixed magnet, the carts KE is momentarily zero and all of the energy in the system is stored in the magnetic field as magnetic potential energy, then rebounds back. The magnetic PE is transformed back to KE.

   Raise one end magnetic of the air track the cart will end up at some equilibrium position, whee the repulsion force between the two magnets will equal the gravitational force component on the cart parallel to the track. Get the angle and hence this component from the geometry of the set up. 

    The air track is frictionless, it also is a factor that effect calculate error. 

Lab#11 Work-Kinetic Energy Theorem Activity

EXPT 1: Work done by a Non-constant Spring Force

  We measure the work done when we stretch a spring through a measured distance. First we will collect data for force applied by a stretched spring vs distance the spring is stretched, and we will plot a graph of force vs distance.Then we will be able to calculate the work done by finding the area under this graph.

Set up
  Set up the ramp, cart, motion detector, force probe, and spring as shown in the diagram, use cart"stops" or something else to support the spring so that it can be horizontal and unstretched. Be sure that the motion detector sees the cart over the whole distance of interest-from the position where the spring is just unstretched to the position.

     we got k = 2.956 N/m, EPE =(1/2)kx^2

Integral: 0.1274 N*m, the work that spring did on cart. 

EXPT 2: Kinetic Energy And The Work-Kinetic Energy Principle

  1. Use the same set up as above.
  2. measure the mass of the cart = 0.571 kg.
  3. be sure that the motion detector sees the cart over the whole distance of interest-from the position where the spring is stretched about 1.0 m to the position where it is just about unstretched. 
  4. Make sure that the x-axis of your graph is "position". Zero the force probe withe the spring hanging loosely. Then pull the cart along the track so that the spring is stretched about 1.0 m from the unstretched position.
  5. Begin graphing, and release the cart, allowing the spring to pull it back at least to the unstretched position. 

    Note that the top graph displays the force applied by the spring on the cart vs. position. It is possible to find the work done by the spring force for the displacement of the cart between any two positions. This can be done by finding the area under the curve using the integration ruutine in the software. The kinetic energy of the cart can be found directly from the bottom graph for any position of the cart.

    The work done by the spring is -0.2799 N*m, and the kinetic energy is 0.057 N*m.

The work done by the spring is -0.3145 N*m, and the kinetic energy is 0.256 N*m

The work done by the spring is -0.1941 N*m, and the kinetic energy is 0.313 N*m

    Find the change in kinetic energy of the cart after it is released from the initial position (where the kinetic energy is zero) to several different final positions.

Conclusions:

    The work done on the cart by the spring is equal to its change in kinetic energy. In any position,

EXPT 3:Work-KE theorem

    On the laptop is a movie file entitled Work-KE  theorem cart and machine for Phys 1.mp4. in the video, the professor uses a machine to pullback on a large rubber band. The force being exerted on the rubber band is recorded by an analog force transducer onto a graph.

    The stretched rubber band is then attached to a cart of known mass. The cart, once released, passes though two photo gates a given distance apart. By knowing the distance and the time interval between the front of the cart passing through the first photogate and then the second photogate, caculat the final speed and thus the final kinetic energy of the cart.At a convenient place in the movie, stop the movie, make a careful sketch the force vs position graph, and determine the work done by the machine in stretching the rubber band in it.

    

Lab#9 Centripetal force with a motor

Purpose:
    To come up with a relationship between the angle θ and the angle speed ω.

• Get the angle theta from looking at the below triangle with hypotenuse L and height H-h
• Get h by putting a horizontal piece of paper until the stopper just grazes the top of it as it passed by.
• Get enough data to test the model by collecting values of h at a variety of ω. Functionally, do this by increasing the voltage to the motor driving the system.

Set up:

  

Conclusion:
    .    1.5759-1.5234 = 0.0525 error is acceptable for us to confirm the relationship( w = a/r) . If we increasing the radius r, then the angle speed ω will decrease, and if we increasing the angle θ，then  the angle speed ω will increasing also. 

Lab#8 Demonstration--Centripetal Acceleration vs. angular frequency

Purpose:

     To determine the relationship between centripetal acceleration and angular speed.

Measurements we will make:

• How long it takes for the disk to make some number of rotations at a range of rotational speed.

• The accelerometer reading corresponding to each rotational speed.

• Distance of the accelerometer from the center of the rotating disk. Measuring the radius by a meter stick showing is 13.8 cm.

Set up:

     Place the accelerometer on the disk. Verify that accelerometer reads 0 in the x and y-directions and -9.8 m/s^2 in the z-direction.

     Spin the disk at some speed. verify that the accelerometer reads 0 in either the x or the y direction and something in the other direction.

    Centripetal acceleration a, t0, t10 are given, we can find the angle speed omega and its square and r.

Data Treatment and Conclusion:

     The measured radius is 13.8 cm compared with the calculate radius 13.71 cm, the error is  0.07%. Those two radius are closed enough for us to determine the relationship  Centripetal Acceleration vs angular frequency is a = r*w^2.

    Because the disk is not perfect flat, it will effect the mean acceleration value. Addition, we neglect air resistance.

Lab#14 Impulse-Momentum activity

EXPT1: Cart "elastic" (bouncing collisions)

Set up

  1. Clamp the dynamics cart to a rod clamped to a lab table. Extend the spring plunger on the dynamics cart.

  2. Mount a force sensor on another dynamics cart.

  3. Set things up such that the stopper of the moving cart hits the plunger of the stationary cart when the moving cart gets close to the end of the track.

  4. Collide the cart with the plunger several times and observe what happens to the spring plunger.

  5. Set up the motion sensor and zero the motion sensor with the mass hanger.

EXPT2: More massive cart "elastic" (bouncing collisions)

  Add 500g on the cart. 

EXPT 3: Impulse-Momentum Theorem in an Inelastic collision

  Remove the dynamics cart from its clamp and replace it with the wooden "wall" and attach a a blob of clay to the wall at the height of the nail, and replacing the rubber stopper with a nail. Leave the extra mass on the cart.

Summary:

  Compare EXPT 1 and EXPT 2, when add the mass, Impulse-Momentum is increasing.Impulse-Momentum is proportional to the mass when the velocity is not change. Compare EXPT 2 and EXPT 3, in elastic collision, the cart will move to the opposite direction after collision, but in inelastic collision, the cart will stop after collision.