course Phy 231 7/3 9:45 019. `query 19*********************************************
.............................................
Given Solution: x component of the vector = magnitude * cos of the angle y component of the vector = magnitude * sin of the angle To get the magnitude and angle from components: angle = arctan( y component / x component ); if the x component is less than 0 than we add 180 deg to the solution To get the magnitude we take the `sqrt of ( x component^2 + y component^2) ** Self-critique (if necessary): OK Self-critique rating #$&* OK ********************************************* Question: `qExplain what we mean when we say that the effect of a force is completely equivalent to the effect of two forces equal to its components. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The components of the force are the 2 legs of a right triangle and you can use those components to find the resultant vector. The Pythagorean Theorem allows you to know the forces in perpendicular directions and then find the angle and the force in 1 direction. The effect of the 2 forces is the same as with 1 force. Confidence rating #$&*: 3
.............................................
Given Solution: `a** If one person pulls with the given force F in the given direction the effect is identical to what would happen if two people pulled, one in the x direction with force Fx and the other in the y direction with force Fy. ** Self-critique (if necessary): OK Self-critique rating #$&* OK ********************************************* Question: `qExplain how we can calculate the magnitude and direction of the velocity of a projectile at a given point. Your solution: Find the x and y components of the velocity vector using the given information Magnitude = sqrt((x velocity)^2 + (y velocity)^2) Angle = arctan (y velocity / x velocity) Confidence rating #$&*: 3
.............................................
Given Solution: `a** Using initial conditions and the equations of motion we can determine the x and y velocities vx and vy at a given point, using the usual procedures for projectiles. The magnitude of the velocity is sqrt(vx^2 + vy^2) and the angle with the pos x axis is arctan(vy / vx), plus 180 deg if x is negative. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK Self-critique rating #$&* OK ********************************************* Question: `qExplain how we can calculate the initial velocities of a projectile in the horizontal and vertical directions given the magnitude and direction of the initial velocity. Your solution: You find the x and y components of the velocity vector. The horizontal initial velocity will be the x component (velocity cos theta) and the vertical initial velocity will be the y component (velocity sin theta). confidence rating #$&* ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution: `a** Initial vel in the x direction is v cos(theta), where v and theta are the magnitude and the angle with respect to the positive x axis. Initial vel in the y direction is v sin(theta). ** Self-critique (if necessary): OK Self-critique rating #$&* OK ********************************************* Question: `qUniv. 8.63 (11th edition 8.58) (8.56 10th edition). 40 g, dropped from 2.00 m, rebounds to 1.60 m, .200 ms contact. Impulse? Ave. force? Your solution: Vf^2 = 0m/ s^2 + 2(9.8m/s^2)(2m) Vf^2 = 39.3m^2/s^2 Vf = 6.26m/s Momentum_before = .04kg * 6.26m/s = .2504 kg m/s Going up: 0m/s ^2 = v0^2 + 2(9.8m/s^2)(-1.6m) V0^2 = 31.36m^2/s^2 V0 = -5.6m/s Change in velocity = -5.6m/s – 6.26m/s = -11.86m/s Change in momentum = impulse = -11.86 m/s * .04kg = -.4744 kg m/s -.4744 kg m/s = Fnet * .200 ms Fnet = -.4744 kg m/s / .0002 s Fnet = -2372 N Confidence rating #$&*: 3
.............................................
Given Solution: `a** You have to find the momentum of the ball immediately before and immediately after the encounter with the floor. This allows you to find change in momentum. Using downward as positive direction throughout: Dropped from 2 m the ball will attain velocity of about 6.3 m/s by the time it hits the floor (v0=0, a = 9.8 m/s^2, `ds = 2 m, etc.). It rebounds with a velocity v0 such that `ds = -1.6 m, a = 9.8 m/s^2, vf = 0. This gives rebound velocity v0 = -5.6 m/s approx. Change in velocity is -5.6 m/s - 6.3 m/s = -11.9 m/s, approx. So change in momentum is about .04 kg * -11.9 m/s = -.48 kg m/s. In .2 millliseconds of contact we have F `dt = `dp or F = `dp / `dt = -.48 kg m/s / (.0002 s) = -2400 Newtons, approx. ** Self-critique (if necessary): OK Self-critique rating #$&* OK "