COFFEE

Two horizontal forces act on a 2.4 kg chopping block that can slide over a frictionless kitchen counter, which lies in an xy plane. One force is F1 = (3.4 N) i + (3.7 N) j. Find the acceleration of the chopping block in unit-vector notation for each of th...

18 years ago

Four balls are suspended by cords. The longer, top cord loops over a frictionless pulley and pulls with a force of magnitude 95 N on the wall to which it is attached. The tensions in the shorter cords are T1 = 56.0 N (between ball A & B), T2 = 46.7 N (bet...

18 years ago

In a pickup game of dorm shuffleboard, students crazed by final exams use a broom to propel a calculus book along the dorm hallway. If the 3.6 kg book is pushed from rest through a distance of 0.90 m by the horizontal 22 N force from the broom and then ha...

18 years ago

Calculate the ratio of the drag force on a passenger jet flying with a speed of 750 km/h at an altitude of 10 km to the drag force on a prop-driven transport flying at one-fifth the speed and half the altitude of the jet. At 10 km the density of air is 0....

18 years ago

A 3.0 kg block, initially in motion, is pushed along a horizontal floor by a force F of magnitude 18 N at an angle = 45° with the horizontal. The coefficient of kinetic friction between the block and floor is 0.25. (Assume the positive direction is to the...

18 years ago

A 17 N horizontal force F pushes a block weighing 6.0 N against a vertical wall. The coefficient of static friction between the wall and the block is 0.68, and the coefficient of kinetic friction is 0.48. Assume that the block is not moving initially. Wil...

18 years ago

A bicyclist travels in a circle of radius 35.0 m at a constant speed of 7.00 m/s. The bicycle-rider mass is 72.0 kg. Calculate the magnitude of the force of friction on the bicycle from the road. Calculate the magnitude of the net force on the bicycle fro...

18 years ago

A certain string can withstand a maximum tension of 43 N without breaking. A child ties a 0.37 kg stone to one end and, holding the other end, whirls the stone in a vertical circle of radius 0.91 m, slowly increasing the speed until the string breaks. Whe...

18 years ago

A stuntman drives a car (without negative lift) over the top of a hill, the cross section of which can be approximated by a circle of radius R = 110 m. What is the greatest speed at which he can drive without the car leaving the road at the top of the hil...

18 years ago

Given two vectors, a and b, such that a + b = a - b, find the magnitude of b. Consider the equation a + b = a - b to be n vector notation and both a and b have components. Subtract the a vector from both sides. You are left with b = -b That can only be tr...

18 years ago

What are the x and y components of a vector a in the xy plane if it's direction is 215 degrees counterclockwise from the positive direction of the x axis and its magnitude is 12.9 m ? you would be in the third quadrant, so both x and y are negative. The v...

18 years ago

At time t1 = 2.00 s, the acceleration of a particle in counterclockwise circular motion is (9.00i + 8.00j) m/s^2. It moves at constant speed. At time t2 = 3.00s (3/4 of a revolution later), it's acceleration is (8.00i - 9.00j) m/s^2. Find the radius of th...

18 years ago

A sphere of mass 2.7 x 10^-4 kg is suspended from a cord. A steady horizontal breeze pushes the sphere so that the cord makes a constant angle of 41 degrees with the vertical. Find the magnitude of the push provided by the breeze and Find the tension in t...

18 years ago

A man (weighing 915 N) stands on a long railroad flatcar (weighing 2805 N) as it rolls at 18.0 m/s in the positive direction of an x axis, with negligible friction. Then the man runs along the flatcar in the negative x direction at 40.00 m/s relative to t...

18 years ago

A vessel at rest at the origin of an xy coordinate system explodes into three pieces. Just after the explosion, one piece, of mass m, moves with velocity (-30 m/s)i and a second piece, also of mass m, moves with velocity (-30 m/s)j. The third piece has ma...

18 years ago

A stationary block explodes into two pieces L and R that slide across a frictionless floor and then into regions with friction, where they stop. Piece L, with a mass of 2.0 kg, encounters a coefficient of kinetic friction µL = 0.40 and slides to a stop in...

18 years ago

"Relative" is an important word. Block L of mass mL = 1.90 kg and block R of mass mR = 0.500 kg are held in place with a compressed spring between them. When the blocks are released, the spring sends them sliding across a frictionless floor. (The spring h...

18 years ago

The rigid body shown in Figure 10-66 (it is a triangle with the upper mass = to M and the bottom two corners/masses equal to 2M. The bottom side length equals .70 cm with point P in the middle of the side and the other two sides equal .55 cm) consists of...

18 years ago

In Figure 11-32 (which shows a ball at the top of an incline, at the bottom of the incline a loop begins with radius R and Q a point on the loop lined up with the center of the loop), a solid brass ball of mass m and radius r will roll without slipping al...

18 years ago

A sanding disk with rotational inertia 1.1 x 10^-3 kg*m^2 is attached to an electric drill whose motor delivers a torque of 6 Nm about the central axis of the disk. What are the following values about the central axis at the instant the torque has been ap...

18 years ago

A 1.1 kg particle-like object moves in a plane with velocity components Vx = 30 m/s and Vy = 90 m/s as it passes through the point with (x, y) coordinates of (3.0, -4.0) m. (a) What is its angular momentum relative to the origin at this moment? _____ kg*m...

18 years ago

Posted by COFFEE on Friday, March 30, 2007 at 4:16am. A sanding disk with rotational inertia 1.1 x 10^-3 kg*m^2 is attached to an electric drill whose motor delivers a torque of 6 Nm about the central axis of the disk. What are the following values about...

18 years ago

Posted by COFFEE on Friday, March 30, 2007 at 4:25am. A 1.1 kg particle-like object moves in a plane with velocity components Vx = 30 m/s and Vy = 90 m/s as it passes through the point with (x, y) coordinates of (3.0, -4.0) m. (a) What is its angular mome...

18 years ago

A particle is acted on by two torques about the origin: T1 has a magnitude of 4.3 N*m and is directed in the positive direction of the x axis, and T2 has a magnitude of 3.2 N*m and is directed in the negative direction of the y axis. What are the magnitud...

18 years ago

An automobile can be considered to be mounted on four identical springs as far as vertical oscillations are concerned. The springs of a certain car are adjusted so that the oscillations have a frequency of 4 Hz. (a) What is the spring constant of each spr...

18 years ago

..im really stuck on this. can someone please explain? ------- Figure A [[which i tried to recreate below]] is a partial graph of the position function x(t) for a simple harmonic oscillator with an angular frequency of 1.1 rad/s. [a].....x(cm)....... .......

18 years ago

Figure A [[which i tried to recreate below]] is a partial graph of the position function x(t) for a simple harmonic oscillator with an angular frequency of 1.1 rad/s. [a] ............x(cm).............. .................5-|-................. ................

18 years ago

When the angular momentum changes, the 'change' in the angular momentum vector (ie. dL) is ____. [a.] perpendicular to the torque vector. [b.] parallel to the angular momentum vector. [c.] parallel to the torque vector. .. im confused on this one.. i thin...

18 years ago

a man is standing on the center of a platform that is rotating without friction. his arms are outstretched holding a brick in each hand. the rotational inertia of the system consists of the man, bricks, and platform about the central vertical axis of the...

18 years ago

An object rotates about a fixed axis, and th angular position of a reference line on the object is given by THETA(t)=0.4e^2t, where THETA is in radians, and t is in seconds. [a.] what is the object's angular acceleration at t = 2 s? ..this is my work so f...

18 years ago

An oscillating block-spring system has a mechanical energy of 1.00 J, an amplitude of 11.2 cm, and a maximum speed of 1.08 m/s. (a) Find the spring constant. ___ N/m (b) Find the mass of the block. ___ kg (c) Find the frequency of oscillation. ___ Hz .. i...

18 years ago

A uniform circular disk whose radius R is 32.0 cm is suspended as a physical pendulum from a point on its rim. (a) What is its period of oscillation? __ s (b) At what radial distance r < R is there a point of suspension that gives the same period? __ cm i...

18 years ago

A performer, seated on a trapeze, is swinging back and forth with a period of 9.55 s. If she stands up, thus raising the center of mass of the trapeze + performer system by 20.0 cm, what will be the new period of the system? Treat trapeze + performer as a...

18 years ago

The angle of the pendulum is given by θ = θmcos(ωt + φ), where ω = 3.24 rad/s. If at t = 0, θ = 1 rad and dθ/dt = -0.9 rad/s, what are φ and θm? So if I substitute in omega and t=0 I have θ = θmcos(φ). How do I solve for phi and omega center of mass???

18 years ago

Two sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a string with a speed of 11 cm/s. If the time interval between instants when the string is flat is 0.33 s, what is the wavelength of the waves? wavelength =...

18 years ago

Calculate the speed of the pulse from the following: y(x,t) = 2/((x - 3t)^2 + 1) Well the speed of the pulse is given by: y(x,t) = f (x - vt) for a pulse traveling to the right and y(x,t) = f (x + vt) for a pulse traveling to the left but in this case the...

18 years ago

Two sinusoidal waves, identical except for phase, travel in the same direction along a string producing a net wave y'(x, t) = (1.5 mm) sin(29x - 4.0t + 0.960 rad), with x in meters and t in seconds. (a) What is the wavelength of the two waves? I found the...

18 years ago

The source of a sound wave has a power of 2.50 µW. Assume it is a point source. (a) What is the intensity 6.70 m away? I used I = Power / 4*pi*r^2 and found I to be 4.43x10^-9 W/m^2 (b) What is the sound level at that distance? Sound level = 10 dB*log [(I...

18 years ago

For two sounds whose sound levels differ by 69 dB, find the ratios (greater value / smaller value) of the following values. (a) the intensities Intensity Final/Intensity Initial = log^-1 (69 / 10) = 7.9x10^6 (b) the pressure amplitudes (c) the particle di...

18 years ago

Two identical tuning forks can oscillate at 329.6 Hz. A person is located somewhere on the line between them. The speed of sound in the air is 343 m/s. Calculate the beat frequency as measured by this individual under the following conditions. (a) the lis...

18 years ago

Integrate: (2x^2+5)/((x^2+1)(x^2+4)) I came up with: (tan^-1)(x)-(1/2)((tan^-1)(2/x)) but it keeps coming back the wrong answer even though I integrated correctly. Is there a way to simplify this answer, and if so, how? Your answer is correct, but I think...

18 years ago

Integrate: 1/(x-sqrt(x+2) dx I came up with: (2/3)(2*ln((sqrt(x+2))-2)+ln((sqrt(x+2))-1)) but it keeps coming back the wrong answer even though I integrated correctly. Is there a way to simplify this answer, and if so, how? I found: Ln[x-sqrt(x+2)] + 1/3L...

18 years ago

How would I solve the following integral with the substitution rule? Integral of: [(x^3)*(1-x^4)^5]dx Put 1-x^4 = y Then -4x^3 dx = dy Integral is then becomes: Integral of -1/4 y^5 dy ok, thanks a lot! I got it now.

18 years ago

How would I evaluate the following integral by using integration by parts? Integral of: (t^3)(e^x)? You mean (x^3)(e^x)? x^3 exp(x) dx = x^3 d[exp(x)] = d[x^3 exp(x)] - exp(x) d[x^3] = d[x^3 exp(x)] - 3 x^2 exp(x) dx So, if you integrate this you get x^3...

18 years ago

How would I integrate the following by parts: Integral of: (x^2)(sin (ax))dx, where a is any constant. Just like you did x^2 exp(x) below. Also partial integration is not the easiest way to do this integral. You can also use this method. Evaluate first: i...

18 years ago

How would I integrate the following: (2x^2 + 5)/((x^2+1)(x^2+4))dx I think I would start with making it a sum of two partial fractions.

18 years ago

Consider a cooling cup of coffee whose initial temperature is 205°. The room temperature is held at 70°. Suppose k = 1/16. Let y be the temperature, and y' its time derivative. ----------------------------------- I have the differential equation: y' = (-1...

18 years ago

find the exact length of this curve: y = ( x^3/6 ) + ( 1/2x ) 1/2 <or= x <or= 1 im looking over my notes, but i'm getting stuck. here's my work so far: A ( 1 , 2/3 ) B ( 1/2 , 49/48 ) y' = [1/6 (3x^2)] + [1/2 (-1x^-2)] y' = ( x^2 / 2 ) - ( x^-2 / 2 ) (y')...

18 years ago

Posted by COFFEE on Monday, June 11, 2007 at 11:48pm. find the exact length of this curve: y = ( x^3/6 ) + ( 1/2x ) 1/2 <or= x <or= 1 im looking over my notes, but i'm getting stuck. here's my work so far: A ( 1 , 2/3 ) B ( 1/2 , 49/48 ) y' = [1/6 (3x^2)]...

18 years ago

i'm still getting this question wrong. please check for my errors: Use Simpson's Rule with n = 10 to estimate the arc length of the curve. y = tan x, 0 <or= x <or= pi/4 .. this is what i did: y' = sec(x)^2 (y')^2 = [sec(x)^2]^2 [f'(x)]^2 = sec(x)^4 Integr...

18 years ago

Graph the curve and find its exact length. x = e^t + e^-t, y = 5 - 2t, from 0 to 3 Length = Integral from 0 to 3 of: Sqrt[(dx/dt)^2 + (dy/dt)^2] dx/dt = e^t - e^-t, correct? dy/dt = -t^2 - 5t, correct? So: Integral from 0 to 3 of Sqrt[(e^t - e^-t)^2 + (-t...

18 years ago

A steady wind blows a kite due west. The kite's height above ground from horizontal position x = 0 to x = 80 ft is given by the following. y = 150 - (1/40)(x-50)^2 Find the distance traveled by the kite. y = 150 - (1/40)(x-50)^2 y = 150 - (1/40)(x-50)(x-5...

18 years ago

The hemispherical tank shown is full of water. Given that water weighs 62.5 lb/ft3, find the work required to pump the water out of the tank. ---------- What is shown is just the tank (a hemisphere) with a radius of 5 ft. ---------- First I calculated the...

18 years ago

Find the exact coordinates of the centroid. y = sqrt[x], y = 0, x = 9. -------------- Is this basically 1/4 of an oval/ellipse? If so then the area would be: pi*9*3, correct? So the X coordinate would equal: 1/Area * Integral from 0 to 9 of (x*f(x))*dx Wh...

18 years ago

Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem below. Give your answer correct to 4 decimal places. y' = 1 - xy y(0) = 0 y(1) = ____ ? ... help, this is what i've done but got the wrong answ...

18 years ago

Use Euler's method with step size 0.2 to estimate y(1.4), where y(x) is the solution of the initial-value problem below. Give your answer correct to 4 decimal places. y' = x - xy y(1) = 0 h = 0.2 Since I am at y(1) = 0 and not y(0) = 0 would I just do thi...

18 years ago

The tank shown is full of water. Given that water weighs 62.5 lb/ft3, find the work required to pump the water out of the tank. The tank shown is a hemisphere with r = 5 ft. The water is to be pumped out at the top. First I solved for ri, ri / (5 - xi) =...

18 years ago

Solve the differential equation. Let C represent an arbitrary constant. (Note: In this case, your answer willto have a negative sign in front of the arbitrary C.) (dz)/(dt) + e^(t+z) = 0 --------------- (dz/dt) + (e^t)(e^z) = 0 (dz/dt) = -(e^t)(e^z) dz =...

18 years ago

Find the exact coordinates of the centroid given the curves: y = 1/x, y = 0, x = 1, x = 2. X = 1/Area*Integral from a to b: x*f(x)dx Y = 1/Area*Integral from a to b: [(1/2)*(f(x))^2]dx How do I find the area for this? Once I know that, is this the correct...

18 years ago

Find the orthogonal trajectories of the family of curves: y = k*(e^-x) --------------- so k = y/(e^-x) differentiating we get: 1 = -k(e^-x)*(dx/dy) 1/(dx/dy) = -k(e^-x) dy/dx = -k(e^-x)...substituting for k: dy/dx = -(y/(e^-x))*(e^-x) dy/dx = -y Integral(...

18 years ago

Given the differential equation: dy/dx = y(1+x), y(0)=1, Use Euler's method with step size .1 to approximate y(.3). y' = y(1+x), y'(0) = 1(1+0)=1 ->the solution has slope 1 at the point (0,1); x0=0, y0=1, h=0.1, F(x,y)=y(1+x) y1=y0+h*F(x0,y0) y1=1 + 0.1(1...

18 years ago

Solve the separable differential equation (dy/dx)=y(1+x) for y and find the exact value for y(.3). dy/dx = y(1+x) dy/y = (1+x)dx Integral (dy/y) = Integral (1+x)dx ln (y) = x + (1/2)x^2 + C y = e^(x + (1/2)x^2 + C) y(0.3) = e^(0.345 + C) I am stuck here....

18 years ago

Please check my work: Find the hydrostatic pressure on one end of a water trough full of water, the end of which is a trapezoid with given dimensions: top of trapezoid = 20 feet, sides of trapezoid both = 8 feet, bottom of trapezoid = 12 feet. Depth of wa...

18 years ago

A force of 27N is required to maintain a spring stretched from its natural length of 12cm to a length of 15cm. How much work is done in stretching the spring from 15 to 25cm? and this is what i did.. please check to see if i did it correctly.. thanks :) f...

18 years ago

Find the average value of the function "f(x) = x^2 sqrt(1+x^3)" on the interval [0,2]. and this is what i did.. please check for mistakes. thanks :D f(x) = x^2 sqrt(1+x^3), [0,2] f ave = (1/(b-a))*inegral of a to b for: f(x) dx f ave = (1/(2-0))*integral...

18 years ago

Find the length of the curve y=(1/(x^2)) from ( 1, 1 ) to ( 2, 1/4 ) [set up the problem only, don't integrate/evaluate] this is what i did.. let me know asap if i did it right.. y = (1/(x^2)) dy/dx = (-2/(x^3)) L = integral from a to b for: sqrt(1+(dy/dx...

18 years ago