One hazard of space travel is debris left by previous missions. There are several thousand masses large enough to detect by radar orbiting the earth, but there are far greater numbers of very small masses such as flakes of paint. Calculate the force exerted by a 0.150 mg chip of paint that strikes a space shuttle window at a relative speed of 4.00 ✕ 103 m/s and sticks, given the collision lasts 6.00 ✕ 10-8 s. Such a collision chipped the window of the ill-fated Challenger in June 1983, causing $50,000 of damage.
To calculate the force exerted by the chip of paint, we can use Newton's second law of motion, which states that force is equal to the change in momentum over time. The equation is as follows:
Force = (change in momentum) / (time)
To find the change in momentum, we first need to calculate the initial and final momentum of the paint chip.
The initial momentum of an object can be calculated using the equation:
Initial Momentum = mass × initial velocity
Let's calculate the initial momentum:
Initial Momentum = (0.150 mg) × (4.00 ✕ 10^3 m/s)
Convert the mass from milligrams to kilograms:
Initial Momentum = (0.150 × 10^(-6) kg) × (4.00 ✕ 10^3 m/s)
Initial Momentum = 6.00 ✕ 10^(-4) kg.m/s
Since the chip is sticking to the window after the collision, the final velocity is zero. Therefore, the final momentum is zero.
Next, let's calculate the change in momentum:
Change in Momentum = Final Momentum - Initial Momentum
Change in Momentum = 0 - 6.00 ✕ 10^(-4) kg.m/s
Change in Momentum = -6.00 ✕ 10^(-4) kg.m/s
Finally, we can calculate the force using the given time duration of the collision:
Force = (-6.00 ✕ 10^(-4) kg.m/s) / (6.00 ✕ 10^(-8) s)
Force = -10 N
The negative sign indicates that the force is acting in the opposite direction to the initial motion.
Since the question asks for the force exerted by the chip of paint, but it is not explicitly mentioned whether it is positive or negative, we can assume the value is positive.
Therefore, the force exerted by the 0.150 mg chip of paint is approximately 10 N.
To calculate the force exerted by the chip of paint on the space shuttle window, we can use the impulse-momentum principle.
The impulse experienced by an object is equal to the change in momentum it undergoes during a collision. The impulse can be calculated using the formula:
Impulse = Change in momentum = Final momentum - Initial momentum
The momentum of an object can be calculated using the formula:
Momentum = Mass × Velocity
Given:
Mass of the paint chip (m) = 0.150 mg = 0.150 × 10^(-6) kg
Relative speed (v) = 4.00 × 10^3 m/s
Collision duration (t) = 6.00 × 10^(-8) s
First, let's calculate the initial momentum of the paint chip. Since the chip sticks to the window, its final velocity will be zero.
Initial momentum (p_initial) = Mass × Initial velocity = m × v
Next, let's calculate the final momentum of the paint chip. As it sticks to the window, its final velocity is zero.
Final momentum (p_final) = Mass × Final velocity = m × 0
Now, the impulse experienced by the paint chip can be calculated as follows:
Impulse (J) = p_final - p_initial
Finally, the force exerted by the chip of paint on the space shuttle window can be calculated using the formula:
Force (F) = Impulse / Collision duration
Let's plug in the values and calculate the force:
m = 0.150 × 10^(-6) kg
v = 4.00 × 10^3 m/s
t = 6.00 × 10^(-8) s
Initial momentum (p_initial) = m × v = 0.150 × 10^(-6) kg × 4.00 × 10^3 m/s
Final momentum (p_final) = m × 0 = 0
Impulse (J) = p_final - p_initial = 0 - (0.150 × 10^(-6) kg × 4.00 × 10^3 m/s)
Force (F) = J / t = (0 - (0.150 × 10^(-6) kg × 4.00 × 10^3 m/s)) / (6.00 × 10^(-8) s)
Now, let's calculate the force using a calculator:
Force (F) = -1.00 × 10^(-3) N
The force exerted by the chip of paint on the space shuttle window is approximately -1.00 × 10^(-3) Newtons (N). The negative sign indicates that the force is in the opposite direction to the motion of the paint chip.
It's important to note that the dollar value of damage caused by the chip of paint can vary depending on the circumstances and repair costs. The given value of $50,000 is provided in the question.
10^3*10^8 = 10^11
force*time=mass*relativespeed
force=.000150Kg*4E3/6E-8=about 10 N
check my math