Answer to Question #294579 in Physics for Kbrom

Question

3. A block of mass m = 2 kg is placed on an inclined plane of angle theta = 30 degrees as shown in Figure 1 The block is released from rest at the top of the plane, where the distance from the bottom is d = 10 m.

(B) How long does it take the block to reach the bottom, and what is its speed just as it gets there?

(A) Find the magnitude of the acceleration of the block and the normal force exerted on the block

Answer 1

(B) The acceleration is

$$a=g\sin\theta,\\\space\\ t=\sqrt{2d/a}=\sqrt{2d/(g\sin\theta)}=2\text{ s},\\ v=\sqrt{2ad}=9.9\text{ m/s}.$$

(A) The magnitude is

$$a=9.8·\sin 30=4.9\text{ m/s}^2.\\ N=mg\cos\theta=17\text{ N}.$$