Vector problems

1. A lift weighs 4000N and has 2 passengers each of weight 700N. What is the tension in the lift cable when the lift is: a) rising at a steady speed, b) moving down at a steady speed.
2. A picture of weight 25N hangs from a hook by two strings which make an angle 35^o with the vertical, What is the tension in each string?
3. A child drags a sledge along horizontal ground at constant velocity by pulling on a rope inclined at 30 degrees to the ground. The drag on the sledge is 50N. What is the tension in the rope?
4. A parent holds a small child in a swing so that the angle of the swing is at 20^o to the vertical. The child's weight is 200N and the swing weighs 50N. What horizontal force must the parent apply?
5. A 1kg camera is supported on a light symmetrical tripod whose legs each make an angle of 25 degrees with the vertical.
(a) What is the compressive force on each leg? (What does compressive mean?)
(b) What horizontal force does each leg exert on the ground?
6. When a pressure of 4.50 N/mm2 is applied to your skin it hurts, each nail in a bed of nails has a point with an area of 1.50 mm².
(a) How much weight can a teacher place on one nail before being hurt?
(b)The teachers weight is 690N. How many nails (at least) should he/she put into the bed?
(c) Explain why he/she must be very careful getting on and off the bed.

Answer:

1. Steady speed so the tension is simple equal to the weight no matter which way the lift is moving.
Tension = 4000 +1400 = 5400 N

2. Upwards forces = downwards forces
2xTcos 35 = 25 So: Tension (T) = 15.3 N

3. Horizontal forces are balanced if the velocity is constant.
Tcos30 = 50 So: Tension (T) = 57.7 N

4. Parent must balance the horizontal forces. In this case it is simply the horizontal component of the tension in the wire supporting the swing.
Vertical forces Tcos 20 = 250 so: Tension(T) = 266 N
Horizontal forces: Force of parent = Tcos 70 = 91 N

5. A compressive force meaning a squashing force tending to make the legs shorter
(a) Vertical forces: 3Tcos 25 = 9.8 So: Tension (T) = 3.6 N
(b) Horizontal force exerted by each leg = Tcos65 = 1.52 N

6. (a) Force = pressure x area = 4.5x1.5 = 6.75 N
(b) Number of nails = 690/6.75 = 102
(c) as they get off they will not be resting on all the hundred and two nails. In fact as they leave the bed they may only be resting on a few and so the force will be very great and therefore very painful!