\fAK + AV + AV = 0 (A) (The force required to compress a spring by a distance x, where k is the Spring Constant (Ni m)) is: F = - kx The work done in compressing the spring by aforce F over a distance x is: W = JFdx As the spring compresses by /x = x2 -x/, this work converts into the potential energy of the spring U = LKAN If the cart is at a height h above some fixed level taken as zero, its Gravitational Potential Energy is: U = mgh As the cart moves, it has akinetic energy given by: K = _myz We will measure the spring constant k, and then squeeze the spring to some extent, to give it spring potential energy. The spring is then released, and it will push a cart up along an inclined plane. When the spring is back to its equilibrium position, the kinetic energy of the cart will be maximum. The cart will keep going up the incline, and the maxi mum height to which the cart goes will determine its maximum gravitational potential energy. We will apply this equation between different points along the path to see how well it holds. X3 Figure 1 X2 XI When the cart is at position *!, the spring is not compressed, and the cart velocity is zero. The cart is then pushed down to X2, and locked at that position by the pin. Using x = X2-X1, the spring potential energy when the spring is compressed to 2 is: (B) The pin is pulled out, the spring is released, and it pushes the cart up the incline. When the cart reaches the point (7, the spring is un-compressed and V/ = 0, and the speed of the cart is maximum. We can find the maximum kinetic energy of the cart from Eqn. (A) as:7. Repeat a few times after adding extra masses to the cart. Use 'Cart Masses" that fit into the space in the launcher (see figure 5) Pull Massas End stops Figure 4. Figure 5. 115 CALCULATIONS 1. During the whole process spring potential energy is converted into kinetic energy, which is then converted into gravitational potential energy Compare these values and find the loss of energy (if argh, and discuss the reasons for the loss. 2. The work done in compressing the spring is the area under the Force-Distance compressed graph 3. The stored potential energy of the spring is found by equation 3. 4. Kinetic energy is found by equation 4 5. The gravitational potential energy of the cart is found by equation 5. 11 6 PRECAUTIONS 1. When using the motion sensor for speed and position make sure that the cart does not come within 20 cm of the motion sensor, else it may give wrongvalues 2. Measure the angle of till of the track carefully, as that angle has a large effect on the value of gravitational Potential Energy 3. Don't forget to add the mass of the mass hanger when finding the spring constant. 4. The shaft of the Spring Cart Launcher should not touch the sides of the holes in the End Stops. 5. Don't mix up the springs. They are color coded so you canidentify them