A ball of mass m moves along a track in the shape of vertical circular loop. There are 2 forces acting on the ball -- the normal force exerted by track (Ntrack) and gravity (mg). Ignore friction and air resistance. The vectors v (velocity) and a (total acceleration) have an angle ◊ between them, which changes as the ball moves. Check all the answers which are true statements. There may be more than one correct answer! when the ball is on the way up the loop, 0 > 90°º the magnitude of a is always smaller than g, no matter how fast the ball moves 0 = 90° at the "side" points (halfway up the loop) at the bottom of the loop, Ntrack is stronger than mg the ball falls off the track if Ntrack = 0

Two masses are connected by a light string that passes over a frictionless pulley, as shown below. The masses are m1 = 6.32 kg, and m2 = 7.51 kg.  If the coefficient of friction between the incline and m2 is 0.232 and the angle of the incline is 35.0°, find (a) acceleration of the two masses, (b) the tension in the string, and (c) the speed of each mass 2.11 s after being released from rest. (d) Also, determine what m2 would have to be in order to have the system accelerate in the direction opposite of what you found in (a).  Assume m1 stays at the same. Note: this problem needs to be done using forces and FBDs - no credit will be given for doing it any other way.

A student is skateboarding down a ramp that is 6.02 m long and inclined at 22.3° with respect to the horizontal. The initial speed of the skateboarder at the top of the ramp is 4.98 m/s. Neglect friction and find the speed at the bottom of the ramp.

In the very Dutch sport of ducth-dude-on-a-pole, athletes run up to a long pole and then use it to vault across a canal. At the very top of his arc, a 70kg vaulter is moving at 3.5m/s and is 5.0m from the bottom end of the pole.  What force would the vaulter exert on the pole (in magnitude)?

A person whirls a 0.250-kg stone in a 1.00-m-radius horizontal circle at the end of a string. The horizontal component of the force with which the person pulls on the string is 5.00 N. Write expressions for the projections of the displacement, velocity, and acceleration on a diameter of the circle.

In the very Dutch sport of ducth-dude-on-a-pole, athletes run up to a long pole and then use it to vault across a canal. At the very top of his arc, a 70kg vaulter is moving at 3.5m/s and is 5.0m from the bottom end of the pole. What vertical force does the pole exert on the vaulter (in magnitude)?

Two masses are connected by a light string that passes over a frictionless pulley, as shown below. The masses are m1 = 6.00 kg, and m2 = 7.00 kg.  If the coefficient of friction between the incline and m2 is 0.200 and the angle of the incline is 35.0°, find (a) acceleration of the two masses, (b) the tension in the string, and (c) the speed of each mass 2.00 s after being released from rest. Also, determine (d) what m2 would have to be in order to have the system accelerate in the direction opposite of what you found in (a).  Assume m1 stays at 6.00 kg.

An 8.00 kg box sits on a ramp that is inclined at 33.0 above the horizontal. The coefficient of kinetic friction between the box and the surface of the ramp is mk = 0.300. A constant horizontal force F = 26.0 N is applied to the box, and the box moves down the ramp. If the box is initially at rest, what is its speed 2.00 s after the force is applied?

A 35.0-kg child swings in a swing supported by two chains, each 2.90 m long. The tension in each chain at the lowest point is 426 N. (a) Find the child's speed at the lowest point.Answer in m/s(b) Find the force exerted by the seat on the child at the lowest point. (Ignore the mass of the seat.)Answer in N (upward)

A plastic disc is flicked up a sloping board. It has an initial speed of 1.6 ms ¹, but gradually slows down. The board is inclined at 18° to the horizontal, and when the disc is flicked its centre is 0.3 m from the top of the board, as shown below. The coefficient of sliding friction between the disc and the board is 0.05. Model the disc as a particle, and take the magnitude of the acceleration due to gravity to be g = = 9.8ms ². 0.3 m 18 j In your response to this question, underline vectors to distinguish them from scalar quantities. If the magnitude of a vector is unknown, use the vector letter to represent the magnitude. For example, write the magnitude of a vector A as A. (a) State the three forces acting on the disc while it is sliding up the board, and draw a force diagram to represent them, labelling each force appropriately and indicating the directions of the forces by marking the sizes of suitable angles. (b) Find expressions for the component forms the three forces, in…