PHYS 142E

Sample test for first midterm exam.

A piece of chalk is thrown straight up; at some point it stops and begins to drop. Can there be a nonzero acceleration at this point even though the velocity falls to zero? [Explain in two or three sentences.] (yes)

 

An electron in the picture tube of a TV set, traveling in a straight line, accelerates uniformly from speed 3 x 104 m/s to 5 x 106 m/s along a length of 2 cm.
  1. How much time does the electron spend in this 2-cm region? (7.95 ns)
  2. What is the magnitude of the electron's acceleration? (6.25 E14 m/s^2)

 

A projectile is launched at an angle of 45 degrees to the horizontal, as shown (launched from the floor, at 5 m/s, one meter from the wall). Find the height H above the ground at which the projectile will strike the wall. (0.606 m)

A sphere is expanding. The radius is increasing at the rate of 1 cm per second. At what rate is the volume increasing, at the particular moment when the radius is 5cm? [State your answer in cm3/s.] (the volume of a sphere is 4/3 pi r^3) (314.2)

A small mass m slides down a frictionless track that makes a circular loop of radius R at the bottom. The mass starts from rest at a height H above the bottom of the loop.
  1. What is the speed of the mass when it first reaches the bottom of the circle? (sqrt(2gH))
  2. If H = 10R, what is the force exerted by the track when the mass reaches the top of the circle? (15 mg down)
  3. If H = 10R, find the maximum distance the spring, of spring constant k, will be compressed.(the spring is at the end of a frictionless straightaway after the mass is again travelling horizontally at ground level) (sqrt(20 mgR/k))
  4. If H = 2R, the mass will not reach the top of the circle. For this situation, find the position, as defined by the angle q , when the mass loses contact with the track. (theta is the counter-clockwise angle above the horizontal segment which goes from the center of the loop to the right side of the loop halfway up; using this convention the top of the loop is at 90 degrees) (41.8 degrees)

The maximum power of a particular horse is 1 hp. With what speed can this horse pull a sled up an 8 degree incline if the weight of the sled with its load is 2000 N and the coefficient of kinetic friction m k = 0.047? [State your answer in m/s with two significant figures. 1 horsepower = 746 Watts] (2.0 m/s)