Chapter 8, Problem 8.22P

A 8g mass is released from rest at C which has a height of 1.2m above the base of a loop-the-loop and a radius of 0.38m. The acceleration of gravity is 9.8 m/s2. a)Find the normal force pressing on the track at A, where A is at the same level as the center of the loop. b) Consider a different situation when the initial height at C has not yet been specified. What is the minimum kinetic energy of the block at B, which is located at the top of the loop, so that the block can pass by this point without falling off from the track?

Areas and circular motion A) Consider a particle moving at a constant speed in a straight line with noforces acting on it. For an arbitrary observer located at a fixed point O, show mathematically that an imaginary line joining the observer to the particle sweeps out equal areas in equal time intervals. B) Consider now instead a particle following a circular trajectory with constant angular velocity and an observer at the centre of the circle. Show that the imaginary line that joins the observer to the particle sweeps out equal areas in equal times.

Q1. The Gravitational force exerted by the sun on the earth holds the earth in an orbit around the sun. Let us assume that the orbit is perfectly circular. The workdone by this gravitational force during a short time interval in which the earth moves through a displacement in its orbital path is a. Zero b. Positive c. Negative d. Impossible to determine Q2. A dart is inserted into a spring-loaded dart gun by pushing the spring in by a distance x. For the next loading the spring is compressed a distance 2x. How much work done is required to load the second dart compare with that required to load the first? a. Four times as much b. Two times as much c. The same d. Half as much e. One-fourth as much Q3. Which of the following statements is true about the relationship between the dot product of two vectors and the product of magnitudes of the vectors? a. A.B is larger than AB b. A.B is smaller than AB c. A.B could be larger or smaller than AB, depending on the angle between the vectors…