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Dominik [7]
3 years ago
7

Two blocks slide without friction. Block 1 has a mass of 1.6 kg and a velocity of +5.5 m/s. Block 2 has a mass of 2.4 kg and a v

elocity of +2.5 m/s. After the collision, block 2 has a velocity of +4.9 m/s. What is the velocity of block 1 after the collision?
Physics
1 answer:
fomenos3 years ago
6 0

Answer:

The velocity of block 1 after the collision is 1.9 m/s.

Explanation:

Hi there!

The momentum of the system composed by the two blocks is conserved (i.e. it remains constant) because no external force is acting on the blocks at the moment of the collision. Then, the momentum of the system before the collision is equal to the momentum after the collision. The momentum of the system is calculated adding the momenta of the two blocks.

initial momentum of the system = final momentum of the system

p1 + p2 = p1´ + p2´

m1 · v1 + m2 · v2 = m1 · v1´ + m2 · v2´

Where:

p1 = initial momentum of block 1.

p2 = initial momentum of block 2.

p1´ = final momentum of block 1.

p2´ = final momentum of block 2.

m1 = mass of block 1.

m2 = mass of block 2.

v1 = initial velocity of block 1 (before the collision).

v2 = initial velocity of block 2.

v1´ = final velocity of block 1.

v2´ = final velocity of block 2.

Let´s write the equation with the data we have:

m1 · v1 + m2 · v2 = m1 · v1´ + m2 · v2´

1.6 kg · 5.5 m/s + 2.4 kg · 2.5 m/s = 1.6 kg · v1´ + 2.4 kg · 4.9 m/s

Solving for v1´:

14.8 kg · m/s = 1.6 kg · v1´ + 11.76 kg · m/s

(14.8 kg · m/s - 11.76 kg · m/s) / 1.6 kg = v1´

v1´ = 1.9 m/s

The velocity of block 1 after the collision is 1.9 m/s.

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The design speed of a multilane highway is 60 mi/hr. What is the minimum stopping sight distance that should be provided on the
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Answer:

Part a: When the road is level, the minimum stopping sight distance is 563.36 ft.

Part b: When the road has a maximum grade of 4%, the minimum stopping sight distance is 528.19 ft.

Explanation:

Part a

When Road is Level

The stopping sight distance is given as

SSD=1.47 ut +\frac{u^2}{30 (\frac{a}{g} \pm G)}

Here

  • SSD is the stopping sight distance which is to be calculated.
  • u is the speed which is given as 60 mi/hr
  • t is the perception-reaction time given as 2.5 sec.
  • a/g is the ratio of deceleration of the body w.r.t gravitational acceleration, it is estimated as 0.35.
  • G is the grade of the road, which is this case is 0 as the road is level

Substituting values

                              SSD=1.47 ut +\frac{u^2}{30 (\frac{a}{g} \pm G)}\\SSD=1.47 \times 60 \times 2.5 +\frac{60^2}{30 \times (0.35-0)}\\SSD=220.5 +342.86 ft\\SSD=563.36 ft

So the minimum stopping sight distance is 563.36 ft.

Part b

When Road has a maximum grade of 4%

The stopping sight distance is given as

SSD=1.47 ut +\frac{u^2}{30 (\frac{a}{g} \pm G)}

Here

  • SSD is the stopping sight distance which is to be calculated.
  • u is the speed which is given as 60 mi/hr
  • t is the perception-reaction time given as 2.5 sec.
  • a/g is the ratio of deceleration of the body w.r.t gravitational acceleration, it is estimated as 0.35.
  • G is the grade of the road, which is given as 4% now this can be either downgrade or upgrade

For upgrade of 4%, Substituting values

                              SSD=1.47 ut +\frac{u^2}{30 (\frac{a}{g} \pm G)}\\SSD=1.47 \times 60 \times 2.5 +\frac{60^2}{30 \times (0.35+0.04)}\\SSD=220.5 +307.69 ft\\SSD=528.19 ft

<em>So the minimum stopping sight distance for a road with 4% upgrade is 528.19 ft.</em>

For downgrade of 4%, Substituting values

                              SSD=1.47 ut +\frac{u^2}{30 (\frac{a}{g} \pm G)}\\SSD=1.47 \times 60 \times 2.5 +\frac{60^2}{30 \times (0.35-0.04)}\\SSD=220.5 +387.09 ft\\SSD=607.59ft

<em>So the minimum stopping sight distance for a road with 4% downgrade is 607.59 ft.</em>

As the minimum distance is required for the 4% grade road, so the solution is 528.19 ft.

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