Answer:
26.5 m/s
Explanation:
The tension in the string provides the centripetal force that keeps the toy in circular motion. So we can write:
where:
T is the tension in the spring
m = 0.50 kg is the mass of the toy
r = 1.0 m is the radius of the circle (the length of the string)
v is the speed of the toy
The maximum tension in the string is
T = 350 N
If we substitute this value into the equation, we find the maximum speed that the mass can have before the string breaks:
Answer:
v₀ = 16.55 m/s
Explanation:
This motion of the ball can be modeled as a projectile motion with following data:
R = Range of Projectile = 27.5 m
θ = Launch Angle = 50°
g = acceleration due to gravity = 9.81 m/s²
v₀ = Initial Speed of Ball = ?
Therefore, using formula for range of projectile, we have:
<u>v₀ = 16.55 m/s</u>
Answer:
The asteroid requires 5.14 years to make one revolution around the Sun.
Explanation:
Kepler's third law establishes that the square of the period of a planet will be proportional to the cube of the semi-major axis of its orbit:
(1)
Where T is the period of revolution and a is the semi-major axis.
In the other hand, the distance between the Earth and the Sun has a value of . That value can be known as well as an astronomical unit (1AU).
But 1 year is equivalent to 1 AU according with Kepler's third law, since 1 year is the orbital period of the Earth.
For the special case of the asteroid the distance will be:
That distance will be expressed in terms of astronomical units:
⇒
Finally, from equation 1 the period T can be isolated:
Then, the period can be expressed in years:
Hence, the asteroid requires 5.14 years to make one revolution around the Sun.