Answer:
310.5 J
Explanation:
The total work done by Martha is equal to the increase in gravitational potential energy of the package, which is equal to

where
(mg) = 45 N is the weight of the package
is the increase in height of the package
The package is carried up 3 flights of stairs, each one with a height of 2.3 m, so the total increase in heigth is

And so, the work done by Martha is

The position of the object at time t =2.0 s is <u>6.4 m.</u>
Velocity vₓ of a body is the rate at which the position x of the object changes with time.
Therefore,

Write an equation for x.

Substitute the equation for vₓ =2t² in the integral.

Here, the constant of integration is C and it is determined by applying initial conditions.
When t =0, x = 1. 1m

Substitute 2.0s for t.

The position of the particle at t =2.0 s is <u>6.4m</u>
Answer:
(a) ω = 1.57 rad/s
(b) ac = 4.92 m/s²
(c) μs = 0.5
Explanation:
(a)
The angular speed of the merry go-round can be found as follows:
ω = 2πf
where,
ω = angular speed = ?
f = frequency = 0.25 rev/s
Therefore,
ω = (2π)(0.25 rev/s)
<u>ω = 1.57 rad/s
</u>
(b)
The centripetal acceleration can be found as:
ac = v²/R
but,
v = Rω
Therefore,
ac = (Rω)²/R
ac = Rω²
therefore,
ac = (2 m)(1.57 rad/s)²
<u>ac = 4.92 m/s²
</u>
(c)
In order to avoid slipping the centripetal force must not exceed the frictional force between shoes and floor:
Centripetal Force = Frictional Force
m*ac = μs*R = μs*W
m*ac = μs*mg
ac = μs*g
μs = ac/g
μs = (4.92 m/s²)/(9.8 m/s²)
<u>μs = 0.5</u>
If an electron, a proton, and a deuteron move in a magnetic field with the same momentum perpendicularly, the ratio of the radii of their circular paths will be:
<h3>How is the ratio of the perpendicular parts obtained?</h3>
To obtain the ratio of the perpendicular parts, one begins bdy noting that the mass of the proton = 1m, the mass of deuteron = 2m, and the mass of the alpha particle = 4m.
The ratio of the radii of the parts can be obtained by finding the root of the masses and dividing this by the charge. When the coefficients are substituted into the formula, we will have:
r = √m/e : √2m/e : √4m/2e
When resolved, the resulting ratios will be:
1: √2 : 1
Learn more about the radii of their circular paths here:
brainly.com/question/16816166
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