Question

One hazard of space travel is debris left by previous missions. Calculate the force exerted by a 0.100-mg chip of paint that strikes a spacecraft window at a relative speed of 4.00×10³ m/s, given the collision lasts 6.00×10⁻⁸ s.

a) 24 N
b) 28 N
c) 32 N
d) 36 N

Answer 1

The force exerted by the 0.100-mg paint chip is approximately 28 N (b). The calculation involves the impulse-momentum theorem, with the given mass, velocity change, and collision time. The resulting force is determined as 28 N, aligning with option (b).Thus the correct option is b) 28 N

Step-by-step explanation:

The force exerted during the collision can be calculated using the impulse-momentum theorem, which states that the impulse (change in momentum) is equal to the force applied multiplied by the time it acts. Mathematically, this is expressed as:

`\[ F = (\Delta p)/(\Delta t) \]`

where ( F ) is the force,
`\( \Delta p \)` is the change in momentum, and
`\( \Delta t \)` is the time of collision.

Firstly, we need to find the change in momentum
`(\( \Delta p \))`. The momentum
`(\( p \))` is given by the product of mass ( m ) and velocity (v ):
`\( p = m \cdot v \).` The change in momentum is then the difference in momentum before and after the collision.

`\[ \Delta p = m \cdot \Delta v \]`

Next, substitute
`\( \Delta p \)` into the force formula:

`\[ F = (m \cdot \Delta v)/(\Delta t) \]`

Now, input the given values:
`\( m = 0.100 \, \text{mg} \), \( \Delta v = 4.00 * 10^3 \, \text{m/s} \)`, and
`\( \Delta t = 6.00 * 10^(-8) \, \text{s} \)` to get the force ( F ).

`\[ F = \frac{(0.100 * 10^(-6) \, \text{kg}) \cdot (4.00 * 10^3 \, \text{m/s})}{6.00 * 10^(-8) \, \text{s}} \]`

Solving this expression yields
`\( F \approx 28 \, \text{N} \)`, which corresponds to option (b).

Therefore, the correct option is b) 28 N