Answer:
r = 5.07 m
Explanation:
given,
velocity of the man , v = 3.43 m/s
centripetal acceleration, a = 2.32 m/s²
magnitude of position of = ?
using centripetal acceleration formula



r = 5.07 m
The magnitude of the position vector relative to rotational axis is equal to 5.07 m.
<h2>
Law 1:</h2><h3>An object already in motion stays in motion, unless acted upon by a force.</h3><h3 /><h2>Law 2:</h2><h3>

</h3><h3>f = forces on an object</h3><h3>m = mass of that object</h3><h3>a = acceleration of that object</h3><h3 /><h2>Law 3:</h2><h3>Everything has an equal and opposite reaction.</h3><h3 /><h3>Hope this helps!</h3>
- Magnitude: 12.1 N.
- Direction: 17.0° to the 8 N force.
<h3>Explanation</h3>
Refer to the diagram attached (created with GeoGebra). Consider the 5 N force in two directions: parallel to the 8 N force and normal to the 8 N force.
.
.
The sum of forces on each direction will be the resultant force on that direction:
- Resultant force parallel to the 8 N force:
. - Resultant force normal to the 8 N force:
.
Apply the Pythagorean Theorem to find the magnitude of the resultant force.
(3 sig. fig.).
The size of the angle between the resultant force and the 8 N force can be found from the tangent value of the angle. Tangent of the angle:
.
Find the size of the angle using inverse tangent:
.
In other words, the resultant force is 17.0° relative to the 8 N force.
Answer:
W = 3.12 J
Explanation:
Given the volume is 1.50*10^-3 m^3 and the coefficient of volume for aluminum is β = 69*10^-6 (°C)^-1. The temperature rises from 22°C to 320°C. The difference in temperature is 320 - 22 = 298°C, so ΔT = 298°C. To reiterate our known values we have:
β = 69*10^-6 (°C)^-1 V = 1.50*10^-3 m^3 ΔT = 298°C
So we can plug into the thermal expansion equation to find ΔV which is how much the volume expanded (I'll use d instead of Δ because of format):

So ΔV = 3.0843*10^-5 m^3
Now we have ΔV, next we have to solve for the work done by thermal expansion. The air pressure is 1.01 * 10^5 Pa
To get work, multiply the air pressure and the volume change.

W = 3.12 J
Hope this helps!