Question

7. An 80-kg man and his car are suddenly accelerated from rest to a speed of 5 m/s
as a result of a rear-end collision. Assuming the time taken to be 0.3s, find:
a) the impulse on the man and
b) the average force exerted on him by the back seat of his car.
8. An airplane propeller is rotating at 1900 rev/min.
a. Compute the propeller's angular velocity in rad/s.
b. How long in seconds does it take for the propeller to turn through 30.0
degrees?
9. A disk with a 1.0-m radius reaches a maximum angular speed of 18 rad/s before
it stops 30 revolutions after attaining the maximum speed. How long did it take
the disk to stop?

Answer 1

Answer on Question #52298, Physics, Other

7. An 80-kg man and his car are suddenly accelerated from rest to a speed of $5\mathrm{m/s}$ as a result of a rear-end collision. Assuming the time taken to be 0.3s, find:

a) the impulse on the man and

b) the average force exerted on him by the back seat of his car.

Solution:

The impulse on the man is

$$p = m v = 80 * 5 = 400 \mathrm{kg} \cdot \mathrm{m/s}$$

If a force $F$ is applied to a particle for a time interval $t$, the momentum of the particle changes by an amount

$$p = F t$$

Thus,

$$F = \frac{p}{t} = \frac{400}{0.3} = 1333.3 \mathrm{N}$$

**Answer:** a) $400\mathrm{kg}\cdot \mathrm{m/s}$; b) $1333.3\mathrm{N}$

8. An airplane propeller is rotating at 1900 rev/min.

a. Compute the propeller's angular velocity in rad/s.

b. How long in seconds does it take for the propeller to turn through 30.0 degrees?

Solution:

a. The conversion between a frequency f measured in hertz and an angular velocity $\omega$ measured in radians per second are:

$$\omega = 2 \pi f$$

We have $f = 1900 \, \text{rev/min} = 1900 / 60 = \frac{95}{3} \, \text{Hz}$

$$\omega = 2 \pi f = 2 \cdot 3.14159 \cdot 95 / 3 = 199 \, \text{rad/s}$$

b. The angle is

$$\varphi = \omega t$$

Thus,

$$t = \frac{\varphi}{\omega} = \frac{30{}^{\circ} * \pi}{180{}^{\circ}} * \frac{1}{199} = 0.0026 \, \text{s}$$

**Answer:** a. 199 rad/s; b. 0.0026 s.

9. A disk with a 1.0-m radius reaches a maximum angular speed of 18 rad/s before it stops 30 revolutions after attaining the maximum speed. How long did it take the disk to stop?

Solution:

$$distance \ traveled = circumference * number \ of \ revolutions$$

Thus,

$$d = 2\pi R * 30 = 60\pi \ m$$

The linear speed is

$$v = R\omega = 1 * 18 = 18 \ \mathrm{m/s}$$

The time is

$$t = \frac{d}{v} = \frac{60\pi}{18} = 10.5 \ \mathrm{s}$$

Answer: 10.5 s.

http://www.AssignmentExpert.com/