Video Discussion: MSTE-00 Problem Set 9

Set 9 Part 1

  1. Determine the minimum value of a force F required to cause an impending motion of a 30 kg block up a 30° incline if the coefficient of friction of the block and the incline is 0.25.
  2. The weight of stone cladding from a large shipment averages 1.5 kg with a standard deviation of 0.162 kg. If these weights are normally distributed, what percent of these cladding would be expected to weigh between 1.5 kg and 1.8 kg?
  3. A machine poured melted chocolate into moulds. The standard deviation of the amount it pours is 0.7 grams, and the mean amount can be set on the machine. The amount poured may be assumed to follow a normal distribution. The machine is to produce bars whose label says 50 g of chocolate. The company’s lawyers want to have no more than 0.5% of bars containing less than the advertised weight. What should the mean be set at?
  4. A radioactive substance is decaying according to the formula x = ke-0.2t where x is the amount of material remaining after t years and k is the initial amount. Find the half-life of this substance.
  5. Evaluate (2 cis 20°)3.

 

Set 9 Part 2

  1. A man made P2,500 quarterly payment to an account earning 1.5% monthly. Find the accumulated amount after 10 years.
  2. A line of levels 9.36 km is run to check the elevation of BM 2 which been found to be 31.388 meters with BM 1 of elevation at sea level. If the backsight and foresight distances are consistently 110 m and 70 m, respectively, determine the corrected elevation of BM 2 considering the effects of curvature and refraction of the earth.
  3. Situation. It is required to layout a simple curve by deflection angles. The curve is to connect two tangents with an intersection angle of 32° and radius of 240 m. The transit is setup at PC which is at Sta 5 + 767.2.
    1. What is the deflection angle of the first station on the curve?
    2. How many stations are there in the curve?
    3. What is the deflection angle of the station just before PT?

 

Set 9 Part 3-1

Situation. Given the following for a parabolic curve: L = 300 m; g1 = -3.2%; g2 = +1.8%. Point of intersection, PI is at elevation 465.92 m.

  1. Find the mid-chord elevation.
  2. Find the elevation of the lowest point.
  3. Find the tangent offset of the 1st quarter point on the curve.

 

Set 9 Part 3-2

Situation. A particle moves along a curve of parametric equations x = e-t, y = 2 cos 3t, z = 2 sin 3t, where t is the time.

  1. Find the position at t = 0.
  2. Find the velocity at t = 0.
  3. Find the acceleration at t = 0.