child of mass m rides on a Ferris wheel as shown in figure (a). The child moves in a vertical circle of radiius 12.2 m at a constant peed of 2.75 m/s. Categorize Because the speed of the child is constant, we can categorize this problem as one involving a particle (the child) -Select , complicated by the gravitational force acting at all times on the child. Analyze Top (Use the following as necessary: m, and g.) We draw a diagram of forces acting on the child at the bottom of the ride as shown in figure (b). The only forces acting on him are the downward gravitational force ,- mg and the upward force n exerted by the seat. The net upward force on the child that provides his centripetal acceleration has a magnitude F m Using the particle in uniform dircular motion model, apply Newton's second law to the child in the radial direction when he is at the bottom of the ride (Use the following as necessary: rand g.): Botnom The forces acting on E - mg- the child at the botmom A child rides on a ferris wheel of the path Solve for the force exerted by the seat on the child (Use the following as necessary: r, v and g. Do not substitute numerical values; use variables only.): - mg + m n Substitute numerical values given for the speed and radius: ot mg Hence, the magnitude of the force n exerted by the seat on the child is-Select- than the weight of the child. (b) Determine the force exerted by the seat on the child at the top of the ride. The forces acting on SOLUTION the child at the top of the path Analyze (Use the following as necessary: m, g, and ) a) Determine the force exerted by the seat on the child at the bottom of the ride. Express your answer in terms of the weight o the child mg. The diagram of forces acting on the child at the top of the ride is shown in figure (c). The net downward force that provides the centripetal acceleration has a magnitude Fetop" SOLUTION Conceptualize Look carefully at figure (a). Based on experiences you may have had on a Ferris wheel or driving over small hills on a roadway, you would expect to feel lighter at the top of the path. Similarly, you would expect to feel heavier at the bottom of the path. At both the bottom of the path and the top, the normal and gravitational forces on the child act in --Select- a circular path at a constant speed. To yield net force vectors with the same magnitude, the normal force at the bottom mus be -Select- v that at the top. v. The vector sum of these two forces gives a force of constant magnitude that keeps the child moving Apply Newton's second law to the child at this position (Use the following as necessary: m, g, and e)

child of mass m rides on a Ferris wheel as shown in figure (a). The child moves in a vertical circle of radiius 12.2 m at a constant peed of 2.75 m/s. Categorize Because the speed of the child is constant, we can categorize this problem as one involving a particle (the child) -Select , complicated by the gravitational force acting at all times on the child. Analyze Top (Use the following as necessary: m, and g.) We draw a diagram of forces acting on the child at the bottom of the ride as shown in figure (b). The only forces acting on him are the downward gravitational force ,- mg and the upward force n exerted by the seat. The net upward force on the child that provides his centripetal acceleration has a magnitude F m Using the particle in uniform dircular motion model, apply Newton's second law to the child in the radial direction when he is at the bottom of the ride (Use the following as necessary: rand g.): Botnom The forces acting on E - mg- the child at the botmom A child rides on a ferris wheel of the path Solve for the force exerted by the seat on the child (Use the following as necessary: r, v and g. Do not substitute numerical values; use variables only.): - mg + m n Substitute numerical values given for the speed and radius: ot mg Hence, the magnitude of the force n exerted by the seat on the child is-Select- than the weight of the child. (b) Determine the force exerted by the seat on the child at the top of the ride. The forces acting on SOLUTION the child at the top of the path Analyze (Use the following as necessary: m, g, and ) a) Determine the force exerted by the seat on the child at the bottom of the ride. Express your answer in terms of the weight o the child mg. The diagram of forces acting on the child at the top of the ride is shown in figure (c). The net downward force that provides the centripetal acceleration has a magnitude Fetop" SOLUTION Conceptualize Look carefully at figure (a). Based on experiences you may have had on a Ferris wheel or driving over small hills on a roadway, you would expect to feel lighter at the top of the path. Similarly, you would expect to feel heavier at the bottom of the path. At both the bottom of the path and the top, the normal and gravitational forces on the child act in --Select- a circular path at a constant speed. To yield net force vectors with the same magnitude, the normal force at the bottom mus be -Select- v that at the top. v. The vector sum of these two forces gives a force of constant magnitude that keeps the child moving Apply Newton's second law to the child at this position (Use the following as necessary: m, g, and e)