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Svetach [21]
3 years ago
6

The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an initial velocity of 23

.5 m/s is h = 2 + 23.5t − 4.9t2 after t seconds. (Round your answers to two decimal places.) (a) Find the velocity after 2 s and after 4 s. v(2) = m/s v(4) = m/s
Physics
1 answer:
Burka [1]3 years ago
8 0

Answer:

a) v(2) = 3.9\,\frac{m}{s}, b) v(4) = -15.7\,\frac{m}{s}

Explanation:

a) The equation for vertical velocity is obtained by deriving the function with respect to time:

v(t) = 23.5 -9.8\cdot t

The velocities at given instants are, respectivelly:

v(2) = 3.9\,\frac{m}{s}

v(4) = -15.7\,\frac{m}{s}

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A pulley system lifts a 1345 n weight a distance of 0.975m. Paul pulls the rope a distance of 3.90m, exerting a force of 375N. A
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A. IMA: 4

The Ideal Mechanical Advantage (IMA) is given by:

IMA = \frac{d_i}{d_o}

where

d_i is the input distance

d_o is the output distance

For the pulley system in this problem, d_i = 3.90 m and d_o = 0.975 m, so the IMA is

IMA=\frac{3.90 m}{0.975 m}=4


B. MA: 3.59

The actual mechanical advantage (AMA), or simply the Mechanical Advantage (MA), is given by

MA=\frac{F_o}{F_i}

where F_o is the output force and F_i is the input force. For the pulley system in this problem, F_i = 375 N and F_o = 1345 N, so the MA is

MA=\frac{1345 N}{375 N}=3.59


C. Efficiency: 89.8 %

The efficiency of a machine is equal to the ratio between the MA and the AMA:

\eta = \frac{MA}{AMA} \cdot 100

Therefore, in this case,

\eta=\frac{3.59}{4}\cdot 100=0.898=89.8 \%

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