1. One type of BB gun uses a spring-driven plunger to blow the BB from its barrel. (a) Calculate the force constant of its plunger's spring if you must compress it 0.2 m to drive the 0.055 kg plunger to a top speed of 25 m/s. k= VN/m (b) What is the magnitude of force that must be exerted to compress the spring? Neglect any dissipative forces. F= N Think & Prepare 1. What is the amplitude of the plunger? Challenge There are two ways to solve this problem. Can you figure out both?

A horizontal spring with force constant  k = 665 N/m  is attached to a wall at one end and to a block of mass  m = 2.35 kg  at the other end that rests on a horizontal surface. The block is released from rest from a position 4.30 cm beyond the spring's equilibrium position. (a) If the surface is frictionless, what is the speed of the block as it passes through the equilibrium position? m/s(b) If the surface is rough and the coefficient of kinetic friction between the box and the surface is  ?k = 0.300,  what is the speed of the block as it passes through the equilibrium position? m/s

OK, once again we have a pendulum, this time of length 1.49 m, which you release from rest at an angle of 41.6 degrees to the vertical. What will be the speed of the pendulum at the instant it reaches an angle of 12.5 degrees above the vertical?     4.08 m/s     2.58 m/s     2.72 m/s     0.83 m/s

A 2.6kg box is sliding along a frictionless horizontal surface with a speed of 1.8m/s when it encounters a spring.  A. Determine the force constant of the spring if the box compresses the spring 7.50cm before coming to rest. B. Determine the initial speed the box would need to be in order to compress the spring by 1.30cm

9 Spaceman Spiff lost his ship's altimeter during a freak meteor storm, but he needs to know when to deploy his retro rockets to insure a safe landing back on earth. Luckily, he has his trusty toy dart gun whose spring has a 110 N/m spring constant. He loads his 7.2 gram suction cup dart, compresses the spring 4.0 cm, takes vertical aim at the cabin ceiling, and shoots. The suction cup dart flies 1.47 meters above its initial spring-compressed position. What is Spiff's altitude above earth? a

The 10-kg block is released with a speed of 5 m/s when the spring is unstretched. The coefficient of kinetic friction between the block and the inclined surface is 0.2. What is the speed of the block when it has slid 1 m down the surface? k = 200 N/m 5 m/s 30° 4.27 m/s O 3.85 m/s O 5.64 m/s O 3.38 m/s O 7.17 m/s

A 2.8 kg box is sliding along a frictionless horizontal surface with a speed of 1.8 m/s when it encounters a spring, (a) Determine the force constant (in N/m) of the spring, if the box compresses the spring 7.5 cm before coming to rest. N/m (b) Determine the initial speed (in m/s) the box would need in order to compress the spring by 1.4 cm. m/s Additional Materials

9. A 7.9 kg object is suspended 10 m above the ground. Directly beneath it is a spring with a spring constant of 6500 N/m. Qualitatively describe what occurs to the energy of the system once the object is released? (Hint: Consider what occurs as the object falls, encounters the spring, and if it will go back up again!)

If the spring constant of a pogo stick is 3500. N/m and the weight of the person on the pogo stick is 700. N, how much is the spring in the bottom of the pogo stick compressed if the person is able to reach a height of 1.75 m above the equilibrium point of the spring? (Choose h = 0 m at the equilibrium point)