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4 years ago

What is the minimum speed needed to fire a champagne cork a distance of 11m?

1 answer:

Crank4 years ago

8 0

To start with solving this problem, let us assume a launch angle of 45 degrees since that gives out the maximum range for given initial speed. Also assuming that it was launched at ground level since no initial height was given. Using g = 9.8 m/s^2, the initial velocity is calculated using the formula:

(v sinθ)^2 = (v0 sinθ)^2 – 2 g d

where v is final velocity = 0 at the peak, v0 is the initial velocity, d is distance = 11 m

Rearranging to find for v0: 
v0 = sqrt (d * g/ sin(2 θ))

v0 = 10.383 m/s

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Use what you know about mass and how you use it to calculate force in the following situation. If each washer has a mass of 4. 9

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Considering the change of units and the definition of weight, the mass of two washers would be 0.0098 kg and if 4 washers are attached to the string, then the applied force on the car will be 0.196 N.

Mass of two washers

If each washer has a mass of 4.9 g, then the mass of two washers will be calculated simply by multiplying the mass of 1 washer by the amount you have of them, in this case 2:

4.9 g×2= 9.8 g

Being 1 kg = 1000 g, you apply the following rule of three to make the change of units: if 1000 g equals 1 kg, 9.8 g equals how many kilograms?

$mass=\frac{9.8 gramsx1 kg}{1000g}$

Solving:

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Finally, the mass of two washers would be 0.0098 kg.

Applied force

On the other side, mass is the amount of matter that a body contains and weight is the action exerted by the force of gravity on the body.

The mass of an object will always be the same, no matter where it is located. Instead, the weight of the object will vary according to the force of gravity acting on it.

Weight is calculated as the product of the object's mass and the value of the gravitational acceleration:

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In this case, you know:

m= 4.9 g×4= 19.6 g= 0.0196 kg → the mass of 4 washers in kilograms
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Replacing:

W= 0.0196 kg× 10 m/s²

Solving:

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Finally, if 4 washers are attached to the string, then the applied force on the car will be 0.196 N.

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