Answer to Question #102010 in Mechanics | Relativity for Christian

Question

1. An arrow accelerates from 0 to 40 m/s in the 0.5 s it is in contact with the bow string. What is the average acceleration?

2. A coastal force of 20 N acts on a mass of (a) 2 kg, (b) 4 kg, (c) 6 kg. What are the resulting acceleration?

3. A 0.5 kg wrench is dropped from a height of 10 m. What is the momentum just before it strikes the floor?

Answer 1

1.The average acceleration

$$a=\frac{\Delta v}{\Delta t}=\frac{40-0}{0.5}=80\:\rm m/s^2$$

2. The Newton's second law states

$$a=\frac{F}{m}$$

Hence

(a) $a=\frac{20}{2}=10\:\rm m/s^2$

(b) $a=\frac{20}{4}=5\:\rm m/s^2$

(c) $a=\frac{20}{6}=3.3\:\rm m/s^2$

3. The momentum

$$p=mv=m\sqrt{2gh}$$ $$=0.5\times \sqrt{2\times 9.8\times 10}=7\:\rm kg\cdot m/s$$