W05D2 Concept Questions Which of the following types of forces can produce a centripetal acceleration? 1. 2. 3. 4. 5. Normal force Frictional force Tension force Gravitational force All of the above Answer: 5. All of the above forces can produce a centripetal acceleration. A normal force producing a centripetal acceleration could be the force of a car door on a person while the car is turning, or the force on the person in the next question. A friction force producing a centripetal acceleration could be the force on a person standing on a rotating platform, or an object on a turntable (pre-CD, pre-I pod). A tension force producing a centripetal acceleration could be an object whirling on the end of a string; we have seen and will see many such examples. Gravitational forces produce centripetal forces all the time; the moon orbiting the earth, the earth or any planet orbiting the sun, … too many examples to list. The “Barrel of Fun” must spin at a certain minimum angular speed in order for a rider of mass m1 to “stick” to the wall. Does this minimum angular speed change for a rider of mass m2 m1 ? 1. Yes 2. No 3. Not enough information to determine. Answer: 2. The normal component N of the contact force that the cylinder wall exerts on the rider pushes the rider toward the center of the orbit and is equal to N m 2 R , where m is the mass of the ride, is the angular velocity and R is the radius of the barrel. The vertical component of the contact force (static friction) supports the rider and hence is equal to its maximum value, fs mg . The normal force must be large enough in magnitude to result in this frictional force, s N s m 2 R mg , or g / Rs , independent of the mass of the rider. Note that in the limit s 0 , the necessary angular speed becomes unboundedly large. A stone attached to a string is whirled in a vertical plane. Let T1 , T2 , T3 and T4 be the tensions at locations 1, 2, 3, and 4 required for the stone to have a given speed v0 at these four locations. What are the relative tensions in the string? 1. T3 T2 T1 T4 2. T1 T2 T3 T4 3. T1 T2 T4 T3 4. None of the above Answer: 3. When the string is in positions 2 and 4, the tension force is directed radially inward and the tension is equal to T2 = T4 mv0 2 / R , where m is the mass of the stone and R is the radius of the circle. When the string is in position 3 the tension and the gravitational force points downward (inward), hence T3 mg mv0 2 / R and thus T3 mv0 2 / R mg T2 T4 . When the string is in position 1, the tension points upward and the gravitational force points downward (outward), hence T3 mg mv0 2 / R and thus T3 mv0 2 / R mg T2 T4 . A puck of mass M is moving in a circle at uniform speed on a frictionless table as shown below. The puck is attached to a massless, frictionless string that passes through a hole in the table and which is in turn attached to a suspended bob, also of mass M , at rest below the table. What is the magnitude of the centripetal acceleration of the moving puck? 1. 2. 3. 4. 5. Less than g Equal to g Greater than g Zero Insufficient information Answer: 2. Since the suspended bob is static, the tension in string is equal to the gravitational force acting on the bob, T Mg . The puck is accelerating inward due to the tensile force of the string acting on the puck, hence T Ma . Thus Mg Ma , or g a .