H1.04. 2022 Forces Answers to Examples, Quizzes _ Mini-tests

1 Answers to Examples, Quizzes & Mini-test [Forces] Quiz The natural length of a spring is Lo. Sketch the graph of elastic force (F) against TOTAL length of the spring (L). Is F proportional to L? Solution: MINI-TEST 1 A force of 16 N is required to stretch a spring a distance of 40 cm from its rest position. A second identical spring is fixed parallel and adjacent to this spring. How much force is required to stretch this pair of springs by 20 cm? My solution: The applied force needs to overcome the total restoring force of the spring. By Hooke’s Law, restoring force is directly proportional to spring’s extension (for the same spring constant); and directly proportional to the spring constant (for the same extension). Thus stretching ONE spring to HALF the distance requires HALF the force (i.e. 8 N). With TWO springs in parallel & identical, the effective spring constant DOUBLES. This DOUBLES the force required (i.e. 16 N). Final answer: 16 N

2 Quiz A drawbridge of length L being is raised by a chain attached as shown. What is the perpendicular distance from O? What is the moment or torque about O? Perpendicular distance between O & the line of action of the force = Moment or torque about O,  = F L sin  Example 6 A picture weighing 40 N is hung by a wire which passes over a small hook. The two parts of the wire are inclined at 60O to each other. Find the tensile force in the wire. Solution: Example 7 (N01/1/5) A light rod is acted upon by three forces P, Q and R. Which diagram could show the position and direction of each of the forces when the rod is in equilibrium? Solution: 60O

3 Example 9 A uniform ladder of length 10 m and weight 200 N leans against a smooth wall so that it is inclined 60o to the horizontal ground. A boy of weight 500 N stands on the ladder ¼ of the way from its lower end. Calculate the normal reaction at the smooth wall and the magnitude and direction of the force acting on the lower end of the ladder. Solution: 60° A B

4 MINI-TEST 2 A uniform bridge, resting horizontally on supports at each end, weighs 4.5 x 10 4 N and is 8.0 m long. Find the force acting downward on each support when the bridge carries a load of 1.0 x 10 4 N placed 2.0 m from one end. My solution: Quiz 1.0 x 104 N 4.5 x 104 N

5 Which object experiences the greatest value of upthrust? Solution: Upthrust = Weight of fluid displaced  B > A  C = D MINI-TESTS 3 What proportion of an iceberg (floating in water) is submerged? [density of ice = 0.92 g / cm3; density of water = 1 g / cm3]

6 My solution: