As the space shuttle orbits the Earth, the shuttle and the astronauts

You are an industrial engineer with a shipping company. As part of the package- handling system, a small box with mass 1.60 kg i

Kisachek [45]

Answer:

v = 0.84m/s, v(max)= 0.997m/s

Explanation:

Initial work done by the spring, where c is the compression = 0.28m:

$W_s = \frac{1}{2}kc^2$

Work lost to friction:

$W_f =\mu mg(c-x)$

Energy:

$E = W_s-W_f=\frac{1}{2}kc^2 -\mu mg(c-x)=\frac{1}{2}mv^2+\frac{1}{2}kx^2$

(a) Solve for v:

$v=\sqrt{\frac{k}{m}(c^2-x^2)-2\mu g(c-x)}$

(b) Solve $\frac{dv}{dx}=0$ for x:

$\frac{dv}{dx}=\frac{\mu g-\frac{k}{m}x}{\sqrt{\frac{k}{m}(c^2-x^2)-2\mu g(c-x)}}$

$\frac{dv}{dx}=0$ if:

$\mu g-\frac{k}{m}x = 0$

$x_{max} = \frac{\mu gm}{k}$

$v_{max}=\sqrt{\frac{k}{m}c^2-2\mu gc+(\mu g)^2\frac{m}{k}}$

6 0

3 years ago

What force does a trampoline have to apply to a gymnast to accelerate her straight up at ? Note that the answer is independent o

Andrew [12]

Answer: Force applied by trampoline = 778.5 N

<em>Note: The question is incomplete.</em>

<em>The complete question is : What force does a trampoline have to apply to a 45.0 kg gymnast to accelerate her straight up at 7.50 m/s^2? note that the answer is independent of the velocity of the gymnast. She can be moving either up or down or be stationary. </em>

Explanation:

The total required the trampoline by the trampoline = net force accelerating the gymnast upwards + force of gravity on her.

= (m * a) + (m * g)

= m ( a + g)

= 45 kg ( 7.50 * 9.80) m/s²

Force applied by trampoline = 778.5 N

5 0

2 years ago

Take another look at lines 2 and 3. Suppose you use distance and time between any pair of neighboring dots to calculate speed:

Nataly [62]

Answer:

Add the two speeds together.

Then, divide the sum by two. This will give you the average speed for the entire trip. So, if Ben traveled 40 mph for 2 hours, then 60 mph for another 2 hours, his average speed is 50 mph.

8 0

3 years ago

Read 2 more answers

Red light of wavelength 633 nm from a helium-neon laser passes through a slit 0.400mm wide. The diffraction pattern is observed

kogti [31]

Answer:

a) $y_{first}=5.3mm$