A horizontal spring-mass system on a horizontal frictionless surface with a spring constant of 67 N/m and a mass of 4 kg has a maximum velocity of 3 m/s. Calculate the maximum compression of the spring-mass system.
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- A crate of mass m1 slides down a well-lubricated hill of height h, with negligible friction. At the bottom, where it is moving horizontally, it collides with another crate, of mass m2, that initially was sitting at rest and that is attached to a wall by a spring of spring constant k that initially is at its equilibrium length. Assume that the spring itself has negligible mass. a)Given that the distance d that the crates compress the spring is d=0.35 m, calculate the speed v2 of the crates immediately after the collision, in units of meters per second. Use the following values:k=950 N/mm1=2.4 kgm2=2.6 kgμ=0.49g=9.8 m/s2 b) What was the speed of the crate of mass m1 just before the collision with the second block, in meters per second? c)What is the height h of the hill, in meters?An elastic cord is 66 cmcm long when a weight of 73 NN hangs from it but is 87 cmcm long when a weight of 190 NN hangs from it.What is the "spring" constant kk of this elastic cord?. A vertical spring with spring constant 250 N/m and whose mass is negligible is loaded with a 0.050 kg ball and it is compressed by 15 cm when "cocked and loaded", then (a) what speed will it give the ball as it just leaves contact with the spring at the spring's equilibrium position and (b) to what height above the original compressed location will the ball reach when it is launched straight up into the air? Include a diagram of the situation.
- A 72kg boy is surfing and catches a wave that gives him an initial speed of 1.60m/s. He then drops through a height of 1.52m, and ends with a speed of 8.50m/s. How much nonconservative work(in kj) was done on the boy?As given in the figure below, a 4 kg block is accelerated from rest by a compressed spring of spring constant 320 N/m. The block leaves the spring at the spring's relaxed length and then travels over a horizontal floor with a coefficient of kinetic friction uk=0.25. The frictional force stops the block in distance D=5 m. Find the original compression distance of the springElevators have many safety features. In the extremely unlikely event that the multiple steel cables supporting the elevator carriage break and the emergency brakes fail to stop it, there is an oil filled piston at the bottom of the elevator shaft to cushion the landing. Model this piston as an ideal spring and assume that the 5,500 kg carriage is initially descending at 10 m/s when it contacts the spring (initially in equilibrium). The spring brings the carriage to rest over 2 m. Use conservation of energy to determine the spring constant. Assume the friction in the system is 4000 N. You need to consider the change in gravitational potential energy for this question.
- A block with mass 300 g is held at rest against a spring with spring con- stant 200 N/m that has been compressed 3 cm from its equilibrium length. The block is released and allowed to slide on a table, and the coefficient of kinetic friction between the block and the Problem 1 table is 0.3. The block slides a short distance on the table and then comes to rest. Assume the block loses contact with the spring when the spring is at its equilibrium length, and that the friction force only acts after the block has lost contact with the spring. (a) How much work does the spring force do on the block? (b) How much work does the kinetic friction force do on the block? (c) After leaving the spring, what distance does the block slide before coming to rest? (d) What speed did the block have after sliding 5 cm from the point it lost contact with the spring?An elastic cord is 72 cmcm long when a weight of 73 NN hangs from it but is 89 cmcm long when a weight of 210 NN hangs from it.What is the "spring" constant kk of this elastic cord?