5. A 25.0-g mass is attached to a vertical spring and it stretches 15.0 cm. It is then stretched an additional 10.0 cm and then released. What is the maximum velocity of the mass? What is its maximum acceleration? Vmax = amax
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- Consider the mass-on-a-spring system as shown in the figure below. The spring has a spring constant of 1.86e+3 N/m, and the block has a mass of 1.39 kg. There is a constant force of kinetic friction between the mass and the floor of 4.71 N. Starting with the spring compressed by 0.117 m from its equilibrium position, how far will the block travel once it leaves the spring? (Assume that block leaves the spring at the spring's equilibrium position, marked x=0 in the figure. Give your answer as the distance from the equilibrium position to the final position of the block.) Hint: How much work must friction do in order to bring the mass to a stop? How much distance is required for friction to do this work? Enter answer here www.m X = 0 Please enter a numerical answer below. Accepted formats are numbers or "e" based scientific notation e.g. 0.23, -2, 1e6, 5.23e-8 Image size: S M L Max mIf the maximum length of the spring is 40 cm, what average friction force opposes the motion of the mass?Consider a mass-spring system. The spring has a spring constant of 2.35e+3 N/m. On the end of the spring is a mass of 0.840 kg. At the moment that the block is at the system's equilibrium position, it has velocity 2.24 m/s. What will be the maximum displacement of the block from equilibrium if we ignore all friction. Please enter a numerical answer below. Accepted formats are numbers or 'e' based scientific notation e g. 0.23.-2. 16, 523-8
- 6. There is air in the cylinder with the piston. The cross-sectional area of the piston is 5cm, the initial volume is 30cm, the pressure is 1 bar, and the temperature is 20℃. As shown in the picture next, the spring constant of the connected spring is ks=100 N/cm, and it is not deformed initially. By applying heat, the cylinder expands and the pressure in the cylinder becomes 4 bar. Answer the following questions. (hint: The relationship between P and V is straight) (1) Find the final volume (expressed in cm^3). (2) Find the expansion work during this process. (3) Find the amount of heat transfer during this process. Show this process on the P-v diagram3. A box (mass = 100 g) is initially connected to a compressed (x = 80 cm) spring (k = 100 N/m) at point A. It was released and started moving along the horizontal surface (μ = 0.2) until it moves up along the inclined surface (μ = 0.3). The box then stops at point D alone the incline. Consider that e = 30 m and 0 = 30°. (a) What is the velocity of the box at point B?) (Ans: 25.24 m/s) (b) What is the change in kinetic energy from point B to point C? (Ans.: -5.88 J) (c) What is the velocity of the box at point C? (Ans.: 22.79 m/s) (d) What is the length of the incline, f? (Ans. 34.88 m) (e) What is the change in gravitational potential energy from point A to point D? (Ans. 17.10 J) www.m 0 Ꭰ A B CPr1. A body of mass m = 2,50 kg is hung on a vertical spring of spring constant k = 90 N/m. At t = 0 the body is displaced from its equilibri- um position downward by distance ro = 13 cm and it is given an initial velocity vo = 78 cm/s also directed downwards. a) Give the displacement r(t) of the body as a function of time. After how much time does the body pass through the equilibrium position first?
- An unknown mass m is attached to two identical springs. Each spring has a stiffness k = 10 N/m and an unstretched length of 3 m. The unknown mass is released from rest when the springs are horizontal and unstretched. The mass reaches its maximum velocity after falling 4 m. Use work-energy to find the maximum velocity.3. A gas spring behaves like a piston-cylinder device. At a certain instant when the piston is at a distance of 0.2 m from the closed end of the cylinder, the gas density is uniform at 20 kg/m³ and the piston begins to move away from the closed end. Find the rate of change of gas density at this instant if gas velocity is proportional to distance from the closed end with a linear variation from zero at the end to 20 m/s of the piston. 0.2 m → 20 m/s Piston -A cigarettes dispenser requires a south African five-rand (R5) coin with a mass of 9.5 g to dispense one cigarette with a mass of 0.2 g. The design of such a cigarette dispenser is based on a helical spring, of negligible mass, which is found to extend 0.1 mm under a mass of 0.2 g. The spring can support a total mass of a coin. As the customer place money on the dispenser, the spring and coin system displace vertically through 4 mm and release. 1.1. Provide a schematic representation of the mass and spring system. 1.2. Calculate the frequency of natural vibration of the dispenser. 1.3. Determine the velocity of the coin when it is 2 mm below its resting position.
- A "turnpike double" (TPD) is a specific configuration of a tractor-trailer where the tractor unit pulls two trailers with a length of up to 48 ft each (the size of a shipping container). In this problem we consider a FedEx tractor-trailer where the two trailers have a total mass of M1 = M2 = 30,000 kg each and the tractor unit has a total mass of M0 = 10,000 kg. The entire tractor-trailer departs forward from rest with an acceleration of 2 m/s2 (in the direction of the FedEx arrow, naturally). Denote the tension in the coupling between the tractor unit and the first trailer as T0 and the tension in the coupling between the two trailers as T12. Note: Assume that only the tractor unit is affected by friction. You do not need to use any coefficients of friction for this problem. You only need Newton's laws of motion for this problem. What is the tension T12 in the coupling between the two trailers?A board sits in equilibrium. On the left end, there is a wire that supports the board from the ceiling, and to the right, there is a sawhorse that supports the board from the ground. The sawhorse is a distance d= 1/5l from the right edge of the board. There is a block with mass ms= 4.5kg that is a distance 3/4l from the right edge of the board. Finally the board has a mass mb= 11kg. c) Write down Newton's 2nd law. Put the equation in terms of mb, ms, g, T, and Fn. Where T is the tension in the wire, and Fn is the normal force of the sawhorse on the board. d) Write down Newton's 2nd Law for rotations. Put the equation in terms of l, mb, ms, g, T, and Fn.The 20-kg block is subjected to the action of the harmonic force F = (90 cos 6t) N, where t is in seconds. (Figure 1) Figure k-400 N/m Sw 20 kg k=400 N/m 00 F-90 cos 6r c-125 N-s/m < 1 of 1 Part A Write the equation which describes the steady-state motion. Express your answer in terms of t. Express your answer using three significant figures. Express the phase radians and the final result in meters. ΠΙΑΣΦ 4 ? m