Question

Please work out 3 clearly and with units. Thanks!

1. A 10-g bullet travels vertically upwards at 1000 m/s, then strikes and passes through a 2.0-kg block initially at rest. The bullet emerges from the block with a speed of 400 m/s because it transfers momentum to the block. (a) How much momentum did the block gain? (b) How fast is the block now moving, and what is its kinetic energy? (c) Using energy considerations only, to what maximum height will the block rise above its initial position? 2. Four identical point particles (1 kg each) are placed at the vertices of a Axis 1 rectangle (4.0 m x 3.0 m, shown here from the side) and held in those positions by four light rods (negligible mass), which form the sides of 3 m a rectangle. (a) What is the moment of inertia of this rigid body 14 m about the axis that passes through one of the particles and is perpendicular to the plane of the rectangle? (b) How much angular momentum and kinetic energy does the array have if it rotates at an angular velocity of 20 rad/s? Determine the minimum area of a flat ice floe (sheet) 100 cm thick if it must support a 1600-kg truck above seawater. Assume the top of the ice is level with the ocean. (Hint: what is the volume of the ice?) Pice = 920 kg/m', psea = 1020 kg/m². Sketch a diagram and label all forces. Calculate a rough approximation of the area of a truck, and compare it to your answer. 4. The fastest recorded pitch in major league baseball is 100.8 mi/hr by Nolan Ryan in 1974. If that pitch were thrown horizontally how far would the ball fall vertically by the time it reached home plate 60 feet away? (Remember your conversions, and please compute your answer completely in English units - do not use MKS units at all! This is a 2-Dimensional problem.) How high should a pitcher's mound be to compensate for this? g=32 ft/s?, 1 mi = 5280 ft. 5. A 1.0 m long string is fixed at both ends and has a linear density of 0.8 g/m. (a) What is the wavelength of the second harmonie? (b) If the second harmonic has a frequency of 400 Hz, what is the wave speed in the string? (c) What tension is needed in order for the second harmonic to have a frequency of 500 Hz? (d) What is the tension needed in order for the first harmonic (also called the un frauency of 500 Hz instead? For full credit, please sketch all waves.

Answer 1

1. A:- Using conservation of momentum

0.010 * 10000 = 0.010 * 400 + 2.0v

v = speed of the block

v = 48 m/s

B:- KE of the block = (1/2)mv²

KE = 2.0 * 48 * 48 /2

KE = 2304 J

C:- Using conservation of energy, sy the max height reached by the block is h, then

mgh = (1/2)mv²

h = 2304/9.8

h = 235.10 m