PART 3. Cart on frictionless tilted track
This part of the lab is mostly analytical. Consider a 250-gram cart loaded with additional 250 grams (for a total mass of 500 grams) sitting on a frictionless track and having zero initial velocity. A string passed over a pulley attached to one end of the track connects the cart with a vertical 50-gram mass hanger. If you arrange this situation in the VirtualLabs environment and keep the track horizontal, you will notice that the cart-hanger system is moving with some constant acceleration. Your objective is to apply the Newton’s Second Law of motion in order to calculate to what angle (let’s call it “critical”) should the track be tilted (made into an incline) to prevent the cart from moving in either direction. In the the experimental worksheet include the free body diagrams for the cart on the tilted track and the hanger, derive the equation for the “critical” angle and calculate its value. Next check your solution with the simulation. Were you able to make the cart still? Explain. Assume the error in the angle is 0.5 °. How does this error affect the behavior of the cart? What acceleration would the system have as a result of 0.5 ° discrepancy in the tilt from the “critical” angle.