nRamps Handout 511.3: Centripetal Acceleration and Problem Solving or the diagram below you are looking down from above at a puck sliding on a frictionless abletop. The puck is sliding at a constant speed along a circular fence and just leaves ontact with the fence at position B. The fence and puck are also frictionless. a) On the top drawing draw vectors and label them for any forces acting parallel to the table top on the puck at positions A and B. b) On the side views below, draw vectors and label them for any forces acting perpendicular to the tabletop. side view at A c) Which of the forces above are inward forces? __ d) Which of the forces above are outward forces? __ e) What would be the equation for the net force on the puck? __ f) On the top drawing at position B draw a line at an inch long showing the path the puck will tr after point B. How do you know? __ g) On the bottom drawing, draw and label a and an acceleration vector on the puck a A and B. h) At position A is the net force on the pu How do you know? __

To answer the questions systematically, let's break them down step by step. I'll provide explanations and solutions for each part of the problem.<br /><br />---<br /><br />### **a) On the top drawing, draw vectors and label them for any forces acting parallel to the tabletop on the puck at positions A and B.**<br /><br />- At position **A**, the puck is in contact with the circular fence. The force acting parallel to the tabletop is the **centripetal force**, which points toward the center of the circle.<br />- At position **B**, the puck just leaves the fence. There are no forces acting parallel to the tabletop because the puck is no longer in contact with the fence.<br /><br />**Answer:**<br />- At **A**: Draw a vector pointing inward (toward the center of the circle) labeled as "Centripetal Force."<br />- At **B**: No force vector is drawn because there are no forces acting parallel to the tabletop.<br /><br />---<br /><br />### **b) On the side views below, draw vectors and label them for any forces acting perpendicular to the tabletop.**<br /><br />- The only forces acting perpendicular to the tabletop are:<br /> - **Gravitational force (Fg)**: Acts downward due to the weight of the puck.<br /> - **Normal force (Fn)**: Acts upward from the tabletop, balancing the gravitational force.<br /><br />**Answer:**<br />- At both **A** and **B**, draw two vectors:<br /> - One pointing downward labeled "Fg" (gravitational force).<br /> - One pointing upward labeled "Fn" (normal force).<br /><br />---<br /><br />### **c) Which of the forces above are inward forces?**<br /><br />- Inward forces are those directed toward the center of the circle. At position **A**, the inward force is the **centripetal force** provided by the fence.<br /><br />**Answer:** Centripetal force at position **A**.<br /><br />---<br /><br />### **d) Which of the forces above are outward forces?**<br /><br />- Outward forces would be directed away from the center of the circle. However, in this scenario, there are no outward forces acting on the puck because the motion is governed by centripetal force.<br /><br />**Answer:** None.<br /><br />---<br /><br />### **e) What would be the equation for the net force on the puck?**<br /><br />The net force on the puck is the centripetal force that keeps it moving in a circular path. The equation for centripetal force is:<br /><br />\[<br />F_{\text{net}} = F_c = \frac{mv^2}{r}<br />\]<br /><br />Where:<br />- \(m\) = mass of the puck,<br />- \(v\) = speed of the puck,<br />- \(r\) = radius of the circular path.<br /><br />**Answer:** \(F_{\text{net}} = \frac{mv^2}{r}\)<br /><br />---<br /><br />### **f) On the top drawing at position B, draw a line an inch long showing the path the puck will travel after point B. How do you know?**<br /><br />- After leaving the fence at position **B**, the puck will move in a straight line tangent to the circular path at the point of release. This is due to Newton's First Law of Motion (inertia), which states that an object in motion will continue in a straight line unless acted upon by an external force.<br /><br />**Answer:**<br />- Draw a straight line tangent to the circle at position **B** to represent the puck's path after leaving the fence.<br /><br />---<br /><br />### **g) On the bottom drawing, draw and label a velocity vector and an acceleration vector on the puck at positions A and B.**<br /><br />- At position **A**:<br /> - The **velocity vector** is tangent to the circular path.<br /> - The **acceleration vector** (centripetal acceleration) points inward toward the center of the circle.<br /><br />- At position **B**:<br /> - The **velocity vector** is tangent to the circular path (same as the direction of motion after leaving the fence).<br /> - There is no **acceleration vector** because the puck is no longer experiencing a centripetal force.<br /><br />**Answer:**<br />- At **A**: Draw a tangent velocity vector and an inward acceleration vector.<br />- At **B**: Draw only a tangent velocity vector.<br /><br />---<br /><br />### **h) At position A, is the net force on the puck zero? How do you know?**<br /><br />- No, the net force at position **A** is not zero. The puck is undergoing circular motion, which requires a net inward force (centripetal force) to keep it moving along the curved path. If the net force were zero, the puck would move in a straight line instead of a circle.<br /><br />**Answer:** No, the net force is not zero at position **A** because the puck is accelerating inward (centripetal acceleration) to maintain its circular motion.<br /><br />---<br /><br />This completes the analysis of the problem. Let me know if you need further clarification!