A 50 gram ball with an initial velocity of 6 hat i + 3 hat j m/s collides with a

Question

A 50 gram ball with an initial velocity of 6 hat i + 3 hat j m/s collides with a wall and rebounds with a velocity of -4 hat i + 5 hat j m/s. What is the impulse (vector) exerted on the ball by the wall? (Give either magnitude and direction or component form.) The only force acting on a 2.0-kg object moving along the x axis is shown, a. Find the impulse for the interval t = 0 to t = 4.0 s. b. If the velocity v_x is +2.0 m/s at t = 0, what is the velocity at t = 4.0 s? c. At what time (in seconds) does object first change its direction of motion? A bullet of mass m = 0.025 kg is fired parallel to an incline and imbeds itself quickly into a block of wood of mass M= 1.50 kg. The block and bullet then slide up the incline, assumed frictionless, and rise a height H = 1.20 m before stopping. Calculate the initial speed of the bullet (just before it hits the wood). A wheel rotating about a fixed axis has an angular position given by theta = 3.0 - 2.0 t^3, where theta is measured in radians and t in seconds. a. In the box at the right, sketch the plot of the angular acceleration versus time for t greaterthanorequalto 0s. Find the angular velocity and angular acceleration of the wheel at t = 4.0 seconds. c. Find the number of revolutions completed in 4.0 seconds. Forces of 5 N, 6N and 10 N act on a body as shown. Calculate the magnitude and ction (cw, ccw) of the net torque on the body about an axis perpendicular to the page ing through point A. cw ccw (circle one)

Explanation / Answer

part a:

angular position=theta=3-2*t^3

angular velocity=w=d(theta)/dt

=-6*t^2

angular acceleration=dw/dt=-12*t

plot:

part b:

at t=4 seconds, angular velocity=-6*t^2 where t=4

=-6*4^2=-96 rad/s

angular acceleration=-12*4=-48 rad/s^2

part c:

angle at t=0 =3 rad

angle at t=4 seconds=3-2*4^3=-125 rad

total angle complete=3-(-125)=128 rad

number of revolutions=total angle/angle per revolution

=128/(2*pi)=20.37

so it has completed 20 revolutions.

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