A mass resting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. It takes 3.0 JJ of work to compress the spring by 0.13 mm . If the spring is compressed, and the mass is released from rest, it experiences a maximum acceleration of 12 m/s2m/s2.  Find the value of the mass. Express your answer to two significant figures and include the appropriate units.

N 2. A horizontal spring is compressed by 25.0 cm. A 640.0 g box is then placed against the spring and then released. After travelling 3.15 m from the release point, the speed of the mass is 5.68 m/s. The coefficient of friction is 0.34. What is the spring constant of the spring? mi Tum Tm =

The figure blow shows the kinetic energy of a simple pendulum versus its angle θ from the vertical.  Note the energy units are in milli-joules.  The vertical axis is set by Ks=4mJ and the mass of the pendulum bob is 0.200 kg.  Determine the length of the pendulum in meters.  Use g = 9.8 N/kg.

A spring-mass system has a spring with spring constant k=85.0 N/m and a 650.0 gram mass on the end of the spring. The surface supporting the mass is frictionless and there is negligible air resistance. When the system is first observed (at time t = 0), the spring is stretched 13.20 cm from its natural length and the velocity of the mass is 1.90 m/s in the +x direction. 1. What is the displacement function x(t) for this motion? 2. If the spring-mass system was placed in a chamber where the air resistance has a drag constant of b = 1.40, what is the frequency of the new system, in rad/s? Round to the nearest hundredth (0.01). Justify your answer using your rationale and equations used.

A 3 kg block attached to a spring with a spring constant of 9 N/m oscillates horizontally on a frictionless table. Its velocity is 7 m/s when x0 = 0.39 m. What is the block's maximum acceleration (in m/s^2)?

You will solve the following problem twice, first using kinematics and second using the ideas of conservation of energy: A mass is attached to a spring with a spring constant of k=11 N/m. The motion of the mass can be described by the equation x(t) = 35 cos (1.2n t), where x(t) is cm. You want to figure out how fast the mass is moving at x = 28 cm. A. Find a solution using the kinematic relationship, v(t) = x(t). B. Find a solution using the principle of conservation of energy: E = KE + U

A spring (k = 1300 N/m) is used to stop a 1320 kg vehicle initially traveling at 4.1 m/s.    How much is the spring displaced in doing this task?  Δx =    m

How do you measure the mass of an astronaut in orbit? (You can't just use a scale!) For the 1973 - 1979 Skylab program (Skylab was a space station that predated the current International Space Station), NASA engineers designed a Body Mass Measuring Device (BMMD). This is essentially a chair of mass m mounted on a spring with a carefully measured spring constant ks = 605.6 N/m. (The other end of the spring is connected to the Skylab itself, which has a mass much larger than the astronaut or the chair, and so remains essentially fixed as the astronaut oscillates.) The period of oscillation of the empty chair is measured to be 0.90149 s. When an astronaut is sitting in the chair, the period is 2.12151 s. What is the astronaut's mass? Please describe your reasoning!

A 25.0 cm long spring is hung vertically from a ceiling and stretches to 30.5 cm when a 6.50 kg mass is hung from its free end. HINT (a) Find the spring constant (in N/m). N/m (b) Find the length of the spring (in cm) if the 6.50 kg weight is replaced with a 165 N weight. cm

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