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A mass hanging from a vertical spring is somewhat more complicated than a mass attached to a horizontal spring because the gravitational force acts along the direction of motion. Therefore, the restoring force of the oscillations is not provided by the spring force alone, but by the net force resulting from both the spring force and the gravitational force. Ultimately, however, the physical quantities of motion (position, velocity, and acceleration) for a vertical mass on a spring exhibit the same oscillations as a horizontal mass on a spring.
A 100 g mass hangs from a vertical spring as shown in the picture. The measuring stick shows us the vertical y position of the bottom of the spring with the origin (y = 0) at the top of the spring. Note that the positive y direction is downward. The 100 g mass is at rest at the position shown (y = 50 cm). The dashed line in the picture (y = 30 cm) indicates the unstretched resting length of the spring. The mass is pulled down 6 cm, stretching the bottom of the spring to y = 56 cm, and then released so that it begins oscillating.
Draw a free body diagram for the mass when it's at the highest point of its oscillation.
What direction is the net force on the mass at this point? If there is no net force, select No direction. ---Select--- Down Up No direction (force is 0)
Use your free body diagram and Newton's second law to find the magnitude of the acceleration that the mass experiences at the highest point of its oscillation (this is the maximum acceleration).
|amax| = _______ cm/s2
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- A block of mass (3 kg) lays on a frictionless plane and is attached to a horizontal spring with a spring constant (8 N/m). The spring is attached to a nearby vertical wall. The minimum distance of the block from the wall during its oscillations is 0.8 m. The maximum distance of the block from the wall during its oscillations is 1.2 m. If we start a stopwatch (t = 0) when the block is at its closest point to the vertical wall, how far the block from the wall after a time t = 5/4 T? A=0.2 m V= 0.326 T= 0.383sarrow_forwardAn object, whose mass is 0.640 kg, is attached to a spring with a force constant of 148 N/m. The object rests upon a frictionless, horizontal surface (shown in the figure below). The object is pulled to the right a distance A = 0.150 m from its equilibrium position (the vertical dashed line) and held motionless. The object is then released from rest. (a) At the instant of release, what is the magnitude of the spring force (in N) acting upon the object? (b) At that very instant, what is the magnitude of the object's acceleration (in m/s?)? m/s2 (c) In what direction does the acceleration vector point at the instant of release? O Away from the equilibrium position (i.e., to the right in the figure). O Toward the equilibrium position (i.e., to the left in the figure). O The direction is not defined (i.e., the acceleration is zero). O You cannot tell without more information.arrow_forwardA mass suspended from a spring is raised a distance of 5 cm above its resting position. The mass is released at time t=0 and allowed to oscillate. After one third of a second, it is observed that the mass returns to its highest position, which was 4.5 cm above its resting position. What is the rate of change of the position of the mass at t = 2.1 seconds? Round your answer to three decimal places.arrow_forward
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- A compact object with a mass of 5.60 kg oscillates at the end of a vertical spring with a spring constant of 2.00 x 10* N/m. The motion is damped by air resistance, and the damping coefficient is b = 3.00 N. s/m. (a) What is the frequency (in Hz) of the damped oscillation? Hz (b) By what percentage does the amplitude of the oscillation decrease in each cycle? % (c) Over what time interval (in s) does the energy of the system drop to 5.00% of its initial value? (d) What If? The atmosphere of Venus is 50 times thicker than that on Earth. If the effect of air resistance on Venus is represented by b = 150 N s/m, recalculate the answers for parts (a) to (c) for this system if it is set in motion in the atmosphere of Venus. What is the frequency (in Hz) of the damped oscillations? Hz What is the percentage decrease in amplitude in each cycle? % What is the time interval (in s) for the energy to drop to 5.00% of its initial value?arrow_forwardA person who weighs 760 N steps onto a spring scale in the bathroom, and the spring compresses by 0.635 cm. (a) What is the spring constant? (b) What is the weight of another person who compresses the spring by 0.314 cm?arrow_forwardAstronauts in space cannot weigh themselves by standing on a bathroom scale. Instead, they determine their mass by oscillating on a large spring. Suppose an astronaut attaches one end of a large spring to her belt and the other end to a hook on the wall of the space capsule. A fellow astronaut then pulls her away from the wall and releases her. The spring's length as a function of time is shown in the figure (Figure 1). Figure L (m) 1.4 1.2 1.0 0.8 0.6 0.4- 0.2 0.0 0 3 < v 6 1 of 1 -t (s)arrow_forward
- A horizontal spring attached to a wall has a force constant of 720 N/m. A block of mass 1.90 kg is attached to the spring and oscillates freely on a horizontal, frictionless surface as in the figure below. The initial goal of this problem is to find the velocity at the equilibrium point after the block is released. (a) What objects constitute the system, and through what forces do they interact? (b) What are the two points of interest? (c) Find the energy stored in the spring when the mass is stretched 6.40 cm from equilibrium and again when the mass passes through equilibrium after being released from rest. x = 6.40 _____ J x = 0 ______J (e) Substitute to obtain a numerical value. (f) What is the speed at the halfway point?arrow_forwardA mass of 0.69 kg is is initially traveling at 6.19 m/s across a horizontal, frictionless surface. It then reaches a spring with a fixed end having a spring constant of 334 N/m that is positioned horizontally and initially at equilibrium. The incoming mass will then contact the spring, compressing it as it comes to rest. What is the speed of the mass upon the spring being compressed by 0.173 m from its equilibrium position?arrow_forwardAstronauts in space cannot weigh themselves by standing on a bathroom scale. Instead, they determine their mass by oscillating on a large spring. Suppose an astronaut attaches one end of a large spring to her belt and the other end to a hook on the wall of the space capsule. A fellow astronaut then pulls her away from the wall and releases her. The spring's length as a function of time is shown in the figure (Figure 1). Figure L (m) W 1.4 1.2- 1.0 0.8 0.6 0.4 0.2 0.0 T 3 1 of 1 -t (s) What is her mass if the spring constant is 270 N/m ? Express your answer with the appropriate units. m = 62 kg Submit Part B Correct V = What is her speed when the spring's length is 0.70 m ? Express your answer with the appropriate units. 0.81 Previous Answers Submit Provido Foodbook ΠΑ m sec Previous Answers Request Answer ?arrow_forward
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