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

Question

A 50 gram ball with an initial velocity of 6i + 3j m/s collides with a wall and rebounds with a velocity of -4i + 5j m/s. What is impulse exerted on the ball by the wall? (Give the magnitude and direction.) The only force acting on a 5.6-kg object moving along the x axis is shown. If the velocity v_x is -3.0 m/s at t = 1.0 what is the velocity at t = 3.5 s? A 12-g bullet moving horizontally strikes and remains in a 3.0 kg block initially at rest on the edge of a table. The table is 80 cm tall. The bullet-block leaves the table and strikes the floor a horizontal distance of 120 cm away from the base of the table. What is the initial speed of the bullet? A wheel rotating about a fixed axis by theta = 3.0 - 2.0 t^3, where theta is measured in radius and to in seconds. Sketch the plot of the angular acceleration versus time. What is the angular acceleration of the wheel at 4.0 seconds? A block of mass m = 5.0 kg and a block of mass m_2 = 4.0 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.20 m and mass M = 3.0 kg. The fixed, wedge-shaped ramp makes an angle of theta = 30.0 degree as shown in the figure. Assume that the surfaces are smooth and the system is released from rest. a) What is the acceleration of mass m_2 as it moves down the incline? b) Through how many revolutions does the pulley turn if m_2 slides for 0.78 seconds?

Explanation / Answer

1) m = 50 g , u = 6 i + 3j , v = -4 i +5 j

impulse = m(v-u)

= 0.05(-4i +5j -6i -3j)

= -0.5 i +0.1j

magnitude = (0.5^2 +0.1^2)^0.5

= 0.51 kg.m/s

diection theta = 180 -arctan(0.1/0.5)

= 169 degrees with positive x axis

2) m = 5.6 kg, vx = -3 m/s, t = 1 s

area under F and t grapgh give impulse

impulse = m(v -u) = (0.5*(12+0)*(3.5 -2))+(0.5*(0+8)(2-1))

5.6(v +3) = (0.5*(12+0)*(3.5 -2))+(0.5*(0+8)(2-1))

v = -0.68 m/s

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