13. 30. 31. A 50.0 kg gymnast carefully steps onto a trampoline and finds that it is depressed vertically 30.0 cm when it supports her mass in equilibrium. Assuming the trampoline has negligible mass and that it vibrates with SHM, find the natural period of oscillation of the gymnast if her feet never leave the trampoline. You are designing a pendulum clock. How far must the centre of mass of the simple pendulum be located from the pivot point of rotation to give the pendulum a period of 1.00 5? Three waves pass the end of a pier in every 12 5. If there is 2.4 m between the wave crests, what is the frequency? If a spring with k = 12.0 N/m is connected to a mass of 230 g and set in motion with an amplitude of 26.0 cm, calculate the speed of the mass as it passes the equilibrium point. A 2.00 kg mass on a spring is extended 0.300 m from the equilibrium position and released. The spring constant is 65.0 N/m. What is the initial potential energy of the spring? What maximum speed does the mass reach? Find the speed of the mass when the displacement is 0.200 m. For the mass in problem 32, find its maximum acceleration. its acceleration when the displacement is 0.20 m. 343) The Minas Basin in the Bay of Fundy has the largest tides in the world (around 15.0 m see b) figures below). Suppose that a device is stretched across the mouth of the bay for 10.0 km. As the floats inside it rise and fall with the tide, their motion is converted to electricity. Suppose that the mechanical linkages of this proposed system are 29.0% efficient. What power would be produced if the period of the tide is 12.0 hours and 32.0 minutes? {i.e. Calculate the power in terms of mass "m".) Compare the value you obtained in a) to the output of a reactor at Ontario's Darlington Nuclear Station (900 MW). (i.e. Calculate the mass of the floats required in order to generate 900 MW.) 35. 35. 37. A 100 kg mass is dropped from 12 m onto a spring with 0.64 cm of recoil. What is the spring constant? Consider a spring of k = 16 N/m connected to a block mass (m) and having an amplitude of motion of 3.7 cm. What is the total energyr of this system? A 5.0 g bullet is discharged at 350 m/s into a massspring System. If the mass is 10 kg and the spring constant is 150 Mm, how far wiil the spring be compressed if the bullet stays in the mass? SPH4U A force of 36 N is applied to a spring with spring constant 72 N/m. The spring releases a 1.0 kg mass down a ramp 2.0 m high. The ramp is frictionless. It then slides through a patch where there is a force of friction of 4.3 N. The patch is 2.0 m long. It then hits a 2.0 kg mass. Mass 1 stops and mass 2 moves off, without friction, hitting a 3.0 kg pendulum with length 1.0 m. This collision is 100% inelastic. Find the height of the pendulum. Diagram is not drawn to scale. m1 Wooow 1.0 kg 1.0 m m2 2.0 m 2.0 kg 3.0 kg * 2.0 m -G= 6.67 x10-11 Nm2 / kg2 k =8.99 x109 Nm2 / C2 9 proton = 1.602 x10-19 C 9 electron =1.602 x10-19 C 9 neutron = 0.000 C m proton =1.67 x10 27 kg m electron =9.11x10-3 kg m neutron =1.67 x10-27 kg 1. Two charged objects have a repulsive force of 0.080 N. The distance separating the two objects is tripled. Determine the new force. 2. Two charged objects have an attractive force of 0.080 N. Suppose that the charge of one of the objects is tripled and the distance separating the objects is tripled. Calculate the new force. 3. Determine the magnitude of the electric force between two electrons separated by a distance of 0.10 nm. 4. Two point charges are separated by a distance r. Determine the factor by which the electric force between them changes when the separation is reduced by a factor of 1.50. 5. Determine the distance of separation required for two 1.00 uC charges to be positioned so that the repulsive force between them is equivalent to the weight (on Earth) of a 1.00 kg mass. 6. Consider an electron and a proton separated by a distance of 1.0 nm. a) Calculate the magnitude of the gravitational force between them. b ) Calculate the magnitude of the electric force between them. C) Explain how the ratio of these gravitational and electric forces would change if the distance were increased to 1.0 m