Acrate of mass 10.6 kg is pulled up a rough incline with an initial speed of 1.51 m/s. the pulling force is 93.0 n parallel to the incline, which makes an angle of 20.1° with the horizontal. the coefficient of kinetic friction is 0.400, and the crate is pulled 5.08 m.
a) how much work is done by the gravitational force on the crate?
b) determine the increase in internal energy of the crate-incline system due friction.
c) how much work is done by the 93.0 n force on the crate?
d) what is the change in kinetic energy of the crate? e) what is the speed of the crate after being pulled 5.08 m?

Anton created a chart listing different types of materials.which best complete the chart? (a)x: copper y: glass(b)x: rubber y: copper(c)x: paper y: silicon(d)x: silicon y: glass

Fft review: linspace, fs, fftshift, nfft 1. generate one second of a cosine of w,-10hz sampled at f, = 100hz and assign it to x. define a tt as your time axis 2. take 64 points fft. 3. as you remember, the dft (which the fft implements) computes n samples of s2t where k-0,1,2, n -1. plot the magnitude of this 64-points fft at range 0 to 63, what do you think of this graph? 4â·to get the x-axis into a hz-frequency form, plot this 64-points fft between-50 to 50 (the 100hz sampling rate) and have n-points between them. 5. according to your figure, what frequency is this cosine wave at? 6. remember that the fft is evaluating from 0 to 2ď€. we are used to viewing graphs from-ď€ to ď€. therefore, you need to shift your graph. 7. now according to your shifted graph. what frequency is this at? 8. note that the spikes have long drop-offs? try a 1024-point dft. note that the peak is closer to 10 and the drop-off is quicker. although, now sidelobes are an issue

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 790 n/m. it is initially at rest on an inclined plane that is at an angle of 28 degrees with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is k = 0.14. in the initial position, where the spring is compressed by a distance of a = 0.18 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. b) if the spring pushes the block up the incline, what distance, l, in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.