After a 5-pound weight is attached to a spring 5 feet long, the spring is 6 feet long. The 5-pound weight is removed and replaced with an 8-pound weight; The entire system is placed in a medium that offers a resistance numerically equal to the instantaneous speed. From t = 0, an external force f(t) = e^-t is applied to the system. Find the equation of motion if the weight is released from a point 1/2 ft below the equilibrium position with an upward velocity of 3 ft/se

After a 5-pound weight is attached to a spring 5 feet long, the spring is 6 feet long. The 5-pound weight is removed and replaced with an 8-pound weight; The entire system is placed in a medium that offers a resistance numerically equal to the instantaneous speed. From t = 0, an external force f(t) = e^-t is applied to the system. Find the equation of motion if the weight is released from a point 1/2 ft below the equilibrium position with an upward velocity of 3 ft/se

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter4: The Laws Of Motion

Section: Chapter Questions

Problem 54P: A student is asked to measure the acceleration of a glider on a frictionless, inclined plane, using...

See similar textbooks

Similar questions

Tarzan plans to cross a gorge by swinging in an arc from a hanging vine. If his arms are capable of exerting a force of 1350 N on the rope, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 78 kg and the vine is 5.2 m long.
A student working on a school project modeled a trampoline as a spring obeying Hookes law and measured the spring constant of a certain trampoline as 4617 N/m. If a child of mass 27.0 kg compresses the trampoline vertically by a maximum of 0.25 m, while bouncing up and down, what is the childs acceleration at the moment of maximum compression?
A student is asked to measure the acceleration of a glider on a frictionless, inclined plane, using an air track, a stopwatch, and a meterstick. The top of the track is measured to be 1.774 cm higher than the bottom of the track, and the length of the track is d = 127.1 cm. The cart is released from rest at the top of the incline, taken as x = 0, and its position x along the incline is measured as a function of time. For x values of 10.0 cm, 20.0 cm, 35.0 cm, 50.0 cm, 75.0 cm, and 100 cm, the measured times at which these positions are reached (averaged over five runs) are 1.02 s, 1.53 s, 2.01 s, 2.64 s, 3.30 s, and 3.75 s, respectively. (a) Construct a graph of x versus t2, with a best-fit straight line to describe the data. (b) Determine the acceleration of the cart from the slope of this graph. (c) Explain how your answer to part (b) compares with the theoretical value you calculate using a = g sin as derived in Example 4.3.
This problem uses the ideal spring force in one dimension. F = -kx, where x is the deviation from equilibrium, and k is the spring constant. Calculate the particle's maximum speed (vmax), with these numbers: k = 2000 N/m = 2000 kg/s2 m = 5 kg (the mass of the particle) x0 = 0.2 m (the initial position) v0 = 5 m/s (the initial velocity)
A shuttlecock is launched from the ground with an initial speed of 38.694 m/s at an angle of 7.4948 degrees with respect to the horizontal. The shuttlecock experiences air resistance with a drag coefficient of 0.1781 in an environment where the air density is 0.9586 kg/m3. If the shuttlecock has a radius of 3.4 cm and a mass of 5.2 grams, what is the maximum height reached by the shuttlecock? Assume that the experiment is done near the surface of the earth.
An elevator weighing 22.200 kN moving downward with constant acceleration travels a distance of 30 m during the interval of t = 0 s to t = 10 s. Find the tension (kN) in the supporting cable during this time assuming the elevator started from rest and neglecting all resistances.0 I need the answer ASAP. Thanks
A 7 kg block measures 9 cm by 15 cm by 27 cm. When it slides on a 15 cm by 27 cm face, it moves with constant speed when pulled horizontally by a force whose magnitude is 15 N. How big a horizontal force must be applied to pull it with constant speed if it slides on a 9 cm by 27 cm face?
A skier traveling 13.2m/s reaches the foot of a steady upward 19.70975 incline and glides 20.29696m up along this slope before coming to rest. What was the average coefficient of friction?
Two blocks are connected by a light string that passes over a frictionless pulley as in the figure. The block of mass 8.94 kg lies on a horizontal surface and is connected to a spring of force constant 229 N/m. The system is released from rest when the spring is unstretched. If the hanging 13.8 kg block falls a distance 0.725 m before coming to rest, calculate the coefficient of kinetic friction between the block m1 and the surface. The acceleration of gravity is 9.8 m/s2 .
A man and his boat have a mass of 150 kg. If the force exerted by the oars in the direction of motion is 70 N and if the resistance (in N) to the motion is equal to thirty times the speed (m/sec) find the speed 15 sec after the boat starts from rest.
A spring with a spring constant k is used to stop the box moving in an inclined plane, with an initial velocity V1 of mass m. The spring is initially compressed 100 mm with the cables. Since the box creates a maximum of x compression in the spring.(a) Find the coefficient of kinetic friction between the surface and the box.(b) Find the velocity of the box when it re-passes its initial position. V1=3.5 m/s m=26 kg s=620 mm x=45 mm α0 = 140
Three masses (m1 = 3 kg, m2 = 9 kg and m3 = 6) hang from three identical springs in a motionless elevator. The springs all have the same spring constant k=333 N/m