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 #64087, Physics / Mechanics | Relativity

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:

a) $p = mv = 80 \, \text{kg} \times 5 \, \text{m/s} = 400 \, \text{kg} \, \text{m/s}$

b) $F = p/t = 400 \, \text{kg} \, \text{m/s} / 0.3 \, \text{s} = 1333 \, \text{N}$

Answer: a) $400\mathrm{kgm / s}$; b) 1333 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) $\omega = 2\pi f = 2 \times 3.14 \times (1900 \, \text{rev/min} / 60) = 198.8 \, \text{rad/s}$

b) $\phi = \omega t; t = \phi / \omega = 30^0 \times \pi / 180^0 \times 198.8 \, \text{rad/s} = 0.0025 \, \text{s}$

Answer: a) 198.8 rad/s; b) 0.0025 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:

t = d/v

v = $\omega R$

d = $2\pi R n$

t = $2\pi R n / \omega R = 2 \times 3.14 \times 30 / 18 \, \text{rad/s} = 10.5 \, \text{s}$

Answer: 10.5 s

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