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In the hydraulic press used in a trash compactor, the radii of the input piston and the output plunger are 6.0 ✕ 10-3 m and 4.5 ✕ 10-2 m, respectively. If the height difference between the input piston and the output plunger can be neglected, what force is applied to the trash when the input force is 330 N.
(a) Define the simple harmonic motion (SHM).
(b) Write down the difference between Periodic and SHM?
(c) Derive the differential equation of SHM. A body is in simple harmonic motion is
having an amplitude of 5 cm and a period of 0.2 s. Calculate the acceleration and
the velocity of the body when the displacement is (a) 5 cm (b) 3 cm (c) 0 cm
What is an example of the first law of thermodynamics? 5.0-g bullet traveling at a
speed of 300 m/s enters a tree and exits the other side with a speed of 150 m/s.
Where did the bullet’s lost kinetic energy go, and how much energy was
transferred?
(b) What is the application of thermodynamics in engineering studies
A 2.50 kg mass is pushed up against a spring (compressing it 0.491 m from its equilibrium) as shown at point A in the diagram below. It is then released and the mass travels along the frictionless surface up the ramp to a point B that is 1.05 above where it started. The mass continues passed B and down the surface to a point , which is 2.15 m below point B. At point the mass has a speed of 7.88 m/s . What is the spring constant of the spring? Please give your final number as a positive with three significant figures. The answer should me in N / m but don't write down any units. Please note that 200 is considered a three sig number by Canvas .
The following data were collected during a short race between two friends. Velocity (m/s) 0 0.5 1 1.5 2 2 4 6 2 0 Time (s) 0 2 4 6 8 10 12 14 16 18 a) Describe the different sections of the graph. b) Determine the acceleration over the first eight seconds. c) Determine the maximum acceleration. d) Using the graph calculate the displacement: i) over the first eight seconds ii) the total race. e) Find the maximum velocity reached by the runner.
- A wave is described by the wave equation: y(x,t)= 18.2cos(8.2x±10.8t) Determine the frequency of the wave.
- Radio waves travel at the speed of light- 300,000 km/s. What is the wavelength of radio waves received at 111.7 MHz on your FM radio dial?
- A wave is described by the wave equation: y(x,t)= 35.5cos(1.2x±4.5t) Determine the amplitude of the wave.
The kinetic energy of 5.0 kg object is initially 35 j. It is then subject to a constant force so that after traveling 9.5 m, its speed is doubled. Find (a)its initial speed (b)its kinetic energy after traveling 9.5 m and (c)the constant force acting on it
At a sharp horizontal circular turn a bus slows down going from 90.0 km/h to 50.0 km/h in the 15.0 s it takes to round the bend. The radius of the curve is 150 m. Assume the bus continues to slow down at the same rate. At the moment the bus speed reaches 50.0 km/h calculate: (i)the magnitude and direction of the tangential acceleration. (ii)the radial acceleration (magnitude and direction). (iii)the magnitude and direction of the total acceleration
A person is jumping from a height h0 = 10 m with zero initial velocity and a cricket ball is thrown directly upward with an initial velocity v0 = 9.8 m/s at the same instant when time t = 0 s as shown in Fig. 1. Consider h = 11.5 m and i and j to be the unit vectors along the X and Y axis. Gravity is acting along the j direction and the magnitude of gravitational acceleration is given by g = 9.81 m/s2 . The red dot on the person represents his center of mass. (a) if the person and the cricket ball consist of a system, find the position and velocity of the center of mass of the system at time t = 0.5 s. (b) If it takes 0.01 seconds for the person to come to complete rest when he hits the ground, calculate the average force acting on the person. (c) Now consider when the person hits the ground, he bends his knees such that the center of mass of his body is lowered by 15 cm. If the maximum force that the bone of his legs can withstand is 50000 N, will he break his legs?
- Determine the period of oscillation of an ideal spring with mass 22.1kg and spring constant 27.8N/m.
- A mass of 9.2kg is attached to an ideal spring having a force constant of 270.3N/m as in the figure. The mass is displaced from its equilibrium position and released. Assume negligible friction. What is the mass' frequency of oscillation?
- A mass of 6.1kg is attached to a spring having a force constant of 219.1N/m as in the figure. The mass is displaced from its equilibrium position and released. Assume a damping force constant b=16.3kg/s, what is the mass' frequency of oscillation?
