*13-100. For a short time, the 250-kg roller-coaster car with passengers is traveling along the spiral track at a constant speed of v= 8 m/s. If the track descends d = 12 m for every full revolution, 0= 27 rad, determine the magnitudes of the - components of force which the track exerts on the car in the r, 0, and z directions. Neglect the size of the car.

A cart has a mass of 1.5 kg. It is given some initial push toward a sensor and is slowed by a hanging mass which makes the cart turn around and speed up as it returns to its original position. This situation is illustrated in the attached image. If the acceleration towards the sensor is 0.5 m/s2 and the accaleration away from the sensor is 0.15 m/s2,  a. draw the free body diagrams for the cart moving towards the sensor and away from the sensor. b. Write Newton's law for both situations and solve for the frictional force and for the force from the hanging mass.

The collar with mass of 0.7 kg is released from rest at position A and travels down the smooth circular rod in the vertical plane. If the velocity of the collar at Point C is 3.3 m, determine the tangential component of acceleration of the collar (in m) at Point C. The spring has a stiffness of k = 140 N and an unstretched length of 0.5 meters. Consider R = 1.7 meters, 0 = 33°, and g =10 A m R/2 D В R

When 0=60°, the boy's center of mass G has a speed of 10 ft/s as he swings to the right. Determine the rate of increase in his speed and the tension in each of the two supporting cords of the swing at that instant. The boy has a weight of 60 lb. 10 í