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1.A 4m x 4m board has a mass of 5.0kg/m^2. In the center of the board is a square hole of 2m x 2m. Find its mass from one edge of the board

2. An object starts from rest and moves in a circle of radius 15 m with acceleration of 15 rad/s^2, when it is at a point diametrically opposite to the starting point, find its total acceleration.

3. A 15 gram bullet is fired straight up at a falling wooden block that is dropped from the top of a building and has a mass 1.8kg. The bullet has a speed of 810 m/s when it strikes the block that has fallen for time t, bullet imbeds in the block, block reverses direction and reaches the top of the building before stopping momentarily and then falls back. Find the time t.

asked Apr 27, 2015

1. the mass should be equal to mass-area-density multiply area. $m=5.0\times (4^2-2^2)$.

2. the total acceleration is a vector sum of centripetal and tangential accelerations. You need to find the angular or linear velocity to determine the centripetal acceleration, which is $a=\frac {v^2}{r}=\omega^2r$

​To find the angular velocity at the moment, one can use $\omega_f^2-\omega_i^2=2\alpha \Delta\theta$

Here $\Delta \theta=\pi$

3. This is a total inelastic collision. So mechanical energy is not conserved but momentum is conserved.

Define up is the positive direct. $mv_1+Mv_2=(m+M)v_3$, where $v_3$ is the velocity right after collision.

Here $v_1=810m/s$, $v_2=-gt$.

The two object together reached the top and stopped there momentarily. Therefore, $v_3$ will be in upward direction and has a magnitude equal to $v_2$  (acceleration is always $g$ -- falling and tossing up will be symmetric if the final and initial speeds are the same).

With a little bit of algebra, the time t can be solved.
answered Apr 28, 2015 by (21,750 points)
@PhysicsDude is this site is not working now . As no question has been recently answered .