Engr Help

Sample Examples ˗ Modified Format ˗ Dynamics Problems

Example 1: A car moves in a plane with a velocity v = ˗ 2i + 4j ft/sec and with an acceleration

of a = i + 3j ft/sec2. At this instant which of the following are true?

a. The car is moving around a curve counteclockwise.

b. The car is moving around a curve clockwise.

c. The car is stationary.

d. The car is driving in a straight line.

e. None of these.

Example 2: A point is moving with position vector r = (t² ˗ 2t) i + (8t ˗ 8e^t) j ft

What is the radius of curvature ρ at t = 0 seconds.

a. 1/2 ft ≤ ρ ≤ 1 ft b. 2 ft ≤ ρ c. 3/2 ft ≤ ρ ≤ 2 ft

d. 1 ft ≤ ρ < 3/2 ft e. 0 ft ≤ ρ< 1/2 ft

Example 3: A biker is speeding around the inside of a cylindrical track as shown in the figure

below. The outer radius of the track is R. The center of mass of the biker/motorcycle is a

distance d from the outer radius of the track’s wall. The coefficient of friction between the

tires and the wall of the track is μ. Find the minimum speed of the biker without sliding

down the wall of the track.

The minimum speed is given by which of the following values?

a. v = √ [g(R+d)/μ] b. v = √ [g(R˗d)/μ] c. v = √ [2g(R˗d)/μ] d. v = √ [g(R˗d)/2μ]