Table 1. Spring Data Suspended Mass (grams) Applied Force |(newtons), F = mg Stretched (cm) Distance Stretched (m) Suspended Mass Distance (kilograms) 0.050 50 0.050x9.8 = 0.49 1.9 0.019 %3D 100 ? ? 4.0 ? | 150 ? ? 6.1 ? 200 ? ? 7.8 ? 250 ? 10.2 Analysis, 1. Use the data recorded in Table 1 to plot a graph of the Applied Force (vertical axis) vs. Distance Stretched (horizontal axis.) Plot the straight line of best fit. Use graph paper and a ruler. You also can use Excel. Note: F = mg, g = 9.8 m/s², mass must be expressed in kilograms, Distance Stretched must be expressed in meters, 1 m = 100 cm; 1 kilogram = 1000 grams 2. Determine the slope of the line in your graph by selecting two points on the line (don't select points from Table 1). This is the value of the spring constant k. Spring Constant = Include units. 8888

When a simple pendulum of mass m is dropped from a maximum height h, it has a maximum speed of Vmax. What is the maximum speed of a mass m/2 with maximum height h/2? Vmax V2 2vmax Vmax Vmax Vтах 2

B, E to I

Harmonic Oscillator: 1.5kg object is connected to a spring with k=100N/m. (assume that there is no friction) If the object is pulled 3cm from equilibrium position, What is the kinetic energy when the displacement is 2cm?

A biologist hangs a sample of mass 0.725 kg on a pair of identical, vertical springs in parallel and slowly lowers the sample to equilibrium, stretching the springs by 0.200 m. Calculate the value of the spring constant of one of the springs.

(a) (b) (c) (d) The figure below shows a pendulum with length L and the angle 0 from the vertical to the pendulum. It can be shown that 0, as a function of time, satisfies the following nonlinear differential equation d²0 g dt² L where g denotes the acceleration due to gravity. + sin 0 0 For small values of 0 we can assume de dt A 0 sin 0 L such that the differential equation can be considered to be linear. Find the equation of motion of the pendulum with length 750 cm if 0 is initially 15° and its initial angular velocity is = 1 rad/s. What is the maximum angle from the vertical? What is the period of the pendulum (the time to complete one back-and-forth swing)? When will the pendulum be vertical from initial position, that is, 0 = 0 ?

A block on the end of a spring is pulled to a position x=A and released from rest. In one full cycle of its motion, through what total distance does it travel? Explain