<span>A = area of styrofoam
M = mass of stryofoam = A*h*rho_s
m = mass of swimmer
Total mass = m + M = m + A*h*rho_s
Downward force = g*(total mass) = g*[m + A*h*rho_s]
The slab is completely submerged.
Buoyant force = g*(mass of water displaced) = g*[A*h*rho_w]
Equate these
g*[m + A*h*rho_s] = g*[A*h*rho_w]
m + A*h*rho_s = A*h*rho_w
A*h*[rho_w - rho_s] = m
A = m/[h*(rho_w - rho_s)]</span>
Answer:
Earth would continue moving by uniform motion, with constant velocity, in a straight line
Explanation:
The question can be answered by using Newton's first law of motion, also known as law of inertia, which states that:
"an object keeps its state of rest or of uniform motion in a straight line unless acted upon by an external net force different from zero"
This means that if there are no forces acting on an object, the object stays at rest (if it was not moving previously) or it continues moving with same velocity (if it was already moving) in a straight line.
In this problem, the Earth is initially moving around the Sun, with a certain tangential velocity v. When the Sun disappears, the force of gravity that was keeping the Earth in circular motion disappears too: therefore, there are no more forces acting on the Earth, and so by the 1st law of Newton, the Earth will continue moving with same velocity v in a straight line.
Explanation:
Below is an attachment containing the solution.
:<span> </span><span>30.50 km/h = 30.50^3 m / 3600s = 8.47 m/s
At the top of the circle the centripetal force (mv²/R) comes from the car's weight (mg)
So, the net downward force from the car (Fn) = (weight - centripetal force) .. and by reaction this is the upward force provided by the road ..
Fn = mg - mv²/R
Fn = m(g - v²/R) .. .. 1800kg (9.80 - 8.47²/20.20) .. .. .. ►Fn = 11 247 N (upwards)
(b)
When the car's speed is such that all the weight is needed for the centripetal force .. then the net downward force (Fn), and the reaction from the road, becomes zero.
ie .. mg = mv²/R .. .. v² = Rg .. .. 20.20m x 9.80 = 198.0(m/s)²
►v = √198 = 14.0 m/s</span>
Ok so it would be late and the relative velocity would be 190 m/s because 200 m/s - 10 m/s is 190 m/s. Hope this helps.
