Answer:
d) v1 = v2 = v3
Explanation:
This can be determined through the principle of energy conservation. We assess the total mechanical energy E=K+U (the sum of kinetic energy and gravitational potential energy) at both the initial and final positions, ensuring they remain constant.
<pInitially, for the three spheres, we have:
Finally, for the three spheres, we see:
<pGiven that
, and since
remains identical for all spheres, it follows that
is identical for all spheres, indicating that
, the final velocity, is equal for each ball.
The answer is 9938.8 km. Explanation: 1 pound-force = 4.48 N. Hence, 30.0 pounds-force = 134.4 N. The gravitational force between Earth and an object on its surface is defined by: Where M denotes Earth’s mass, m is the object's mass, and R represents the Earth's radius (6371 km). To determine height (h) above Earth's surface, we compare ratios. Ultimately, Pete's weight would be 30 pounds at a height of 9938.8 km from the Earth's surface.
<span>3.834 m/s.
To solve this problem, we must ensure that the centripetal force equals or exceeds the gravitational force acting on the object. The formula for centripetal force is
F = mv^2/r
while the equation for gravitational force is
F = ma.
Since the mass (m) cancels out in both equations, we can equate them, leading to
a = v^2/r.
Now, inserting the given values (where the radius is half the diameter) allows us to find v:
9.8 m/s^2 <= v^2/1.5 m,
which simplifies to
14.7 m^2/s^2 <= v^2.
Therefore, we find that the minimum velocity required is 3.834057903 m/s <= v.
Thus, the necessary speed is 3.834 m/s.</span>
We start by finding the angle of inclination with the sine function,
sin θ = 1 m / 4 m
θ = 14.48°
Next, we compute the work done by the movers using the following formula:
W = Fnet * d
We need to first determine Fnet. It is the weight force minus the frictional force.
Fnet = m g sinθ – μ m g cosθ
Fnet = 1,500 sin14.48 – 0.2 * 1,500 * cos14.48
Fnet = 84.526 N
The work done is therefore:
W = 84.526 N * 4 m
<span>W = 338.10 J</span>
