A spring-loaded dart gun is used to shoot a dart straight up into the air. When fully compressed, the dart reaches a maximum height of h₁ above its release point. The same dart is shot up a second time from the same gun, but this time the spring is compressed at 1/2.14 as compared to the first shot. How high, h₂, does the dart go the second time in terms of the maximum height h₁? Fill in the missing factor below. (Neglect friction and assume the spring is ideal.) [Hint: Use the first situation to find an expression for the spring constant. Use that expression to solve for the height in the second situation.] h₁ h₂

A 3.0 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 4.7 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 1.5 cm. m/s Additional Materials O Reading

A 1.30 kg block slides on a frictionless horizontal surface until it encounters a spring with a force constant of 520 N/m. The block comes to rest after compressing the spring by the distance of 2.50 cm.What was the initial speed of the block ? O 0.25 m/s 5.0 m/s O 31.6 m/s O 0.50 m/s

A ball of mass m is launched straight upward from a spring of constant k compressed by a distance x. Neglecting viscosity and drag, what is the maximum height reached by the ball? Answer choices: A. kx/mg B. mgx C. ½ k x^2 /mg D. mgx/kg

Problem 6: A child's toy consists of a m = 42 g monkey suspended from a spring of negligible mass and spring constant k. When the toy monkey is first hung on the spring and the system reaches equilibrium, the spring has stretched a distance of x = 16.1 cm, as shown in the diagram. This toy is so adorable you pull the monkey down an additional d = 4.1 cm from equilibrium and release it from rest, and smile with delight as it bounces playfully up and down. Unstretched Position Equilibrium Stretched Position Part (a) Using the given information, determine the spring constant, k, in Newtons per meter, of the spring. Numeric : A numeric value is expected and not an expression. k = 2.557 Part (b) Select the free-body diagram that best represents the forces acting on the monkey as you are pulling it down, immediately before you let go. SchematicChoice : F. AF, spring spring spring F. F. F gravity .F applied applied F, A F spring spring F. Fopplied spring F E. gravity F. gravit gravity applied…

A 900 kg safe is 1.5 m above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 40 cm. What is the spring constant of the spring? Express your answer to two significant figures and include the appropriate units.

A horizontal spring with stiffness 0.8 N/m has a relaxed length of 16 cm (0.16 m). A mass of 22 grams (0.022 kg) is attached and you stretch the spring to a total length of 29 cm (0.29 m). The mass is then released from rest. What is the speed of the mass at the moment when the spring returns to its relaxed length of 16 cm (0.16 m)? m/s

An athlete stretches a spring an extra 20.5 cm beyond its initial length. How much energy has he transferred to the spring, if the spring constant is 29.6 N/cm? 622 J 62.2 kJ 62.2 J O 622 kJ