By analysing Hooke’s expression, what can you say about the force when: x = 0 [2] When : x > 0 [2] When : x < 0
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By analysing Hooke’s expression, what can you say about the force
when: x = 0 [2]
When : x > 0 [2]
When : x < 0
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- When a 2.10-kg object is hung vertically on a certain light spring described by Hooke's law, the spring stretches 2.98 cm. (a) What is the force constant of the spring? (b) If the 2.10-kg object is removed, how far will the spring stretch if a 1.05-kg block is hung on it? (c) How much work must an external agent do to stretch the same spring 7.00 cm from its unstretched position?Determine the magnitude and direction of the force F=(690 lb)i +(300 lb)j – (580 lb)k.A 8 kg particle is in a potential given by U(x) = 1 x^4 - 7 x^2 - 3 x + 8 (J). Calculate the acceleration of the particle when it is at x = 1 m, in m/s2. (Please answer to the fourth decimal place - i.e 14.3225)
- (a) A bathroom scale has a spring that is compressed by 1.50 cm when a 150 kg person stands on the scale. Assuming the spring is described by Hooke's law, find its force constant (in N/m). ______N/m (b) How much (in mm) would it be compressed if a 95.0 kg person stands on the scale in an elevator that is accelerating upward at 1.25 m/s²?______mmDesign a "bungee jump" apparatus for adults. A bungee jumper falls from a high platform with two elastic cords tied to the ankles. The jumper falls freely for a while, with the cords slack. Then the jumper falls an additional distance with the cords increasingly tense. Assume that you have cords that are 8 m long, and that the cords stretch in the jump an additional 22 m for a jumper whose mass is 100 kg, the heaviest adult you will allow to use your bungee jump (heavier customers would hit the ground). (a) It will help you a great deal in your analysis to make a series of 5 simple diagrams, like comic strip, showing the platform, the jumper, and the two cords at the following times in the fall and the rebound: 1 while cords are slack (shown here as an example to get you started) 2 when the two cords are just starting to stretch 3 when the two cords are half stretched 4 when the two cords are fully stretched 5 when the two cords are again half stretched, on the way up On each diagram,…Consider the 3-dimensional force field ⃗ F = (x^2 − ze^y)⃗i + (y^3 − xze^y)⃗j + (z^4 − xe^y)⃗k:(a) Show that ⃗ F is conservative.(b) If ⃗ F is conservative, find the corresponding potential function f (x, y).(c) If an object travels on a path ⃗r (t), (t_0 < t < t_f ), does the work done bythe force field depend on the path taken? Find the work done on the object movingon the path ⃗r (t) by the force field ⃗ F , if ⃗r (t_0) = (3, 1, 2) and ⃗r (t_f ) = (6, 2, 5)
- When a 2.30-kg object is hung vertically on a certain light spring described by Hooke's law, the spring stretches 2.26 cm. (a) What is the force constant of the spring? N/m (b) If the 2.30-kg object is removed, how far will the spring stretch if a 1.15-kg block is hung on it? cm (c) How much work must an external agent do to stretch the same spring 7.10 cm from its unstretched position?+962 7 7691 4986 9 minutes ago 40 The potential energy of a diatomic molecule (a two-atom system like H, or O2) is given by B A U = 712 where r is the separation of the two atoms of the molecule and A and B are positive constants. This potential energy is associated with the force that binds the two atoms together. (a) Find the equilib- rium separation-that is, the distance between the atoms at which the force on each atom is zero. Is the force repulsive (the atoms are pushed apart) or attractive (they are pulled together) if their separa- tion is (b) smaller and (c) larger than the equilibrium separation?