A 500 g block is released from rest and slides down africtionless track that begins h = 1.80 m above the horizontal, as shown in Figure. At the bottom of the track, where the surface ishorizontal, the block strikes and sticks to a light spring with aspring constant of 25.0 N/m. Find themaximum distance the spring is compressed.
A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 8.50 N is applied. A 0.530-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x = 5.00 cm and released from rest at t = 0. (Assume that the direction of the initial displacement is positive.)
(a) What is the force constant of the spring? 280 N/m
(b) What are the angular frequency (?), the frequency, and the period of the motion?
? = 23.121 rad/s
f = 3.6817 Hz
T = 0.27161 s
(c) What is the total energy of the system? 0.35 J
(d) What is the amplitude of the motion? 5 cm
(e) What are the maximum velocity and the maximum acceleration of the particle?
(f) Determine the displacement x of the particle from the equilibrium position at t = 0.500 s.
(g) Determine the velocity and acceleration of the particle when t = 0.500 s. (Indicate the direction with the sign of your answer.)
v = _________________
a = _________________
If a tank holds 5000 gallons of water, which drains from the bttomof the tank in 40 minutes, then torricelli's Law gives the volume Vof water remaining in the tank after t minutes .
Find the rate at which water is draining from the tank after (a) 5min, (b) 10 min. At what time is the water flowing out the fastest?the slowest?
In an inkjet printer, letters are built up by squirting drops of ink horizontally at a sheet of paper from a rapidly moving nozzle. The Pattern on the paper is controlled by an electrostatic valve that determines at each nozzle position whether ink is squirted onto thepaper or not. The ink drops have a radius 15.0 and leave the nozzle and travel horizontally toward the paper at speed v=18.0 m/s . The drops pass through a charging unit that gives each drop a positive charge by causing it to lose some electrons. The drops then pass between parallel deflecting plates of length cm , where there is a uniform vertical electric field with magnitude N/C
If a drop is to be deflected a distance d= 0.270 mm by the time it reaches the end of the deflection plate,what magnitude of charge q must be given to the drop? (Assume that the density of the ink drops 1000 , and ignore the effects of gravity.)
A 0.50 kg ball that is tied to the end of a 1.1 m light cord is revolved in a horizontal planewith the cord making a angle, with the vertical.
a) Determine the ball speed.
b) If, instead, the ball is revolved so that its speed is 4.0 m/s,what angle does the cord make with the vertical?
c) If the cord can withstand a maximum tension of 9.1 N, what is the highest speed at which the ballcan move?
An extreme skier, starting from rest, coasts down a mountainthat makes an angle with the horizontal. The coefficient of kinetic friction between her skis and the snow is 0.200. She coasts for a distance of 11.9 m before coming to the edge of a cliff. Without slowing down, she skis offthe cliff and lands down hill at a point whose vertical distance is 4.20 m below the edge. How fast is she going just before she lands?
Ropes 3m and 5m in length are fastened to a holiday decoration that is suspended over a town square. The declaration has a mass of 5kg. The ropes, fastened at different heights, make angles of 52 degrees and 40 degrees with the horizontal. Find the tension in each wire and the magnitude of each tension.
Problem: A 0.500kg block attached to a spring with the length 0.60m and force constant k=40.0 N/m is at rest with the back of the block at point A on a frictionless, horizontal airtable. The mass of the spring is negligible. You pull the block tothe right along the surface with a constant horizontal forceF=20.0-6N.
A.) What is the blocks
A lunch tray is being held in one hand, as the drawing illustrates. The mass of the tray itself is 0.200 kg, and its center of gravity is located tits geometrical center. On the tray is a 1.00 kg plate of food and a 0.190 kg cup of coffee. Obtain the force T exerted by the thumb and the force F exerted by the four fingers. Both forces act perpendicular to the tray, which is being held parallel to the ground.
An 80.0-kg skydiver jumps out of a balloon at an altitude of1000 m and opens the parachute at an altitude of 200 m. (a) Assuming that the total retarding force on the diver is constant at 50.0 N with the parachute closed and constant at 3600 N with the parachute open, what is the speed of the diver whenhe lands on the ground? (b) Do you think the skydiver will be injured? Explain. (c) At what height should the parachute be opened so that the final speed of the skydiver when he hits the ground is 5.00m/s? (d) How realistic is the assumption that the total retarding force is constant? Explain.