Smallest 2 A3 kg object on a rough surface with coefficient of kinetic friction 0.4 is pushed by a constant spring force directly to the right. The spring has a spring constant of 74. If the mass started at rest, and has a final velocity of 1.0 m after 2s, how far is the spring compressed? Type your answer...

When a 3.0-kg block is pushed against a massless spring of force constant constant 4.5103N/m , the spring is compressed 8.0 cm. The block is released, and it slides 2.0 m (from the point at which it is released) across a horizontal surface before friction stops it. What is the coefficient of kinetic friction between the block and the surface?

Review. This problem extends the reasoning of Problem 41 in Chapter 9. Two gliders are set in motion on an air track. Glider 1 has mass m1 = 0.240 kg and moves to the right with speed 0.740 m/s. It will have a rear-end collision with glider 2, of mass m2 = 0.360 kg, which initially moves to the right with speed 0.120 m/s. A light spring of force constant 45.0 N/m is attached to the back end of glider 2 as shown in Figure P9.41. When glider 1 touches the spring, superglue instantly and permanently makes it stick to its end of the spring. (a) Find the common speed the two gliders have when the spring is at maximum compression. (b) Find the maximum spring compression distance. The motion after the gliders become attached consists of a combination of (1) the constant-velocity motion of the center of mass of the two-glider system found in part (a) and (2) simple harmonic motion of the gliders relative to the center of mass. (c) Find the energy of the center-of-mass motion. (d) Find the energy of the oscillation.

A 0.250-kg block along a horizontal track has a speed of 1.50 m/s immediately before colliding with a light spring of force constant 4.60 N/m located at the end of the track. (a) What is the springs maximum compression if the track is frictionless? (b) If the track is not frictionless, would the springs maximum compression be greater than, less than, or equal to the value obtained in part (a)?

Check Your Understanding Find x(t) for the mass-spring system in Example 8.11 ii the particle starts from x0=0 at t=0. what is the particle’s initial velocity?

Fish are hung on a spring scale to determine their mass. (a) What is the force constant of the spring in such a scale if it the spring stretches 8.00 cm for a 10.0 kg load? (b) What is the mass of a fish that stretches the spring 5.50 cm? (c) How far apart are the half-kilogram marks on the scale?

Describe a system in which elastic potential energy is stored.

A 2.00-kg object hangs, at rest, on a 1.00-m-long string attached to the ceiling. A 100-g mass is fired with a speed of 20 m/s at the 2.00-kg mass, and the 100.00-g mass collides perfectly elastically with the 2.00-kg mass. Write an equation for the motion of the hanging mass after the collision. Assume air resistance is negligible.

Hanging from the ceiling over a baby bed, well out of baby’s reach, is a string with plastic shapes, as shown here. The string is taut (there is no slack), as shown by the straight segments. Each plastic shape has the same mass m , and they are equally spaced by a distance d , as shown. The angles labeled describe the angle formed by the end of the string and the ceiling at each end. The center length of sting is horizontal. The remaining two segments each form an angle with the horizontal, labeled . Let T1 be the tension in the leftmost section of the string, T2 , be the tension in the section adjacent to it, and T3 be the tension in the horizontal segment. (a) Find an equation for the tension in each section of the string in terms of the variables m,g , and . (b) Find the angle in terms of the angle . (c) If =5.10 , what is the value of ?(d) Find the distance x between the endpoints in terms of d and .

Consider an undamped linear oscillator with a natural frequency ω0 = 0.5 rad/s and the step function a = 1 m/s2. Calculate and sketch the response function for an impulse forcing function acting for a time τ = 2π/ω0. Give a physical interpretation of the results.