1.) jet plane traveling 1800 km/h (500 m/s) pulls out of a dive by moving in an arc of radius 6.00 km. What is the plane's acceleration in g's?
6.) A child on a merry -go-round is moving with a speed of 1.35 m/s when 1.20 m from the center of the merry-go-round.
a.) calculate centripetal acceleration of the child
b.) the net horizontal force exerted on the child (mass= 25.0 kg).
500^2 m/s /6000m = 41.67 this is acceleration
g= 9.8m/s^2
41.67m/s^2 / 9.8m/s^2 = 4.25 g
1) a = v^2/r
6) same as 1), F = ma
1.) To find the plane's acceleration in g's, we first need to calculate its centripetal acceleration.
The centripetal acceleration (a) can be calculated using the formula:
a = v^2 / r
where v is the velocity and r is the radius of the arc.
Given that the velocity (v) of the plane is 500 m/s and the radius (r) is 6.00 km (or 6000 m), the centripetal acceleration can be calculated as:
a = (500 m/s)^2 / 6000 m
a ≈ 41.67 m/s^2
To convert this acceleration to g's, we can divide it by the acceleration due to gravity (9.8 m/s^2).
Acceleration in g's = (41.67 m/s^2) / (9.8 m/s^2)
Acceleration in g's ≈ 4.25 g's
Therefore, the plane's acceleration is approximately 4.25 g's.
6.) a.) To calculate the centripetal acceleration of the child on the merry-go-round, we can use the same formula as before:
a = v^2 / r
Given that the child's speed (v) is 1.35 m/s and the distance from the center (r) is 1.20 m, the centripetal acceleration can be calculated as:
a = (1.35 m/s)^2 / 1.20 m
a ≈ 1.52 m/s^2
b.) To find the net horizontal force exerted on the child, we can use the formula:
F = m * a
Given that the mass (m) of the child is 25.0 kg and the centripetal acceleration (a) is 1.52 m/s^2, the net horizontal force can be calculated as:
F = (25.0 kg) * (1.52 m/s^2)
F ≈ 38.0 N
Therefore, the net horizontal force exerted on the child is approximately 38.0 N.
To calculate the acceleration in g's in the first scenario, we need to convert the velocity from meters per second to kilometers per hour.
1.) The plane's velocity is given as 500 m/s. To convert this to km/h, we multiply by 3.6:
Velocity = 500 m/s * 3.6 km/h = 1800 km/h.
Now let's calculate the acceleration in g's.
The acceleration of an object moving in a circle is given by the formula:
Acceleration = (Velocity^2) / Radius.
Substituting the given values:
Radius = 6.00 km = 6000 m
Velocity = 1800 km/h = 500 m/s.
Acceleration = (500 m/s)^2 / 6000 m = 41.67 m/s^2.
To convert this to g's, we divide by the acceleration due to gravity, 9.8 m/s^2:
Acceleration in g's = 41.67 m/s^2 / 9.8 m/s^2 ≈ 4.25 g's.
Therefore, the plane's acceleration is approximately 4.25 g's.
6.)
a.) To calculate the centripetal acceleration of the child, we use the formula:
Acceleration = (Velocity^2) / Radius.
The radius is given as 1.20 m, and the velocity is given as 1.35 m/s.
Acceleration = (1.35 m/s)^2 / 1.20 m = 1.51875 m/s^2.
Therefore, the centripetal acceleration of the child is approximately 1.52 m/s^2.
b.) To calculate the net horizontal force exerted on the child, we use Newton's second law:
Force = Mass * Acceleration.
The mass is given as 25.0 kg, and the acceleration is the centripetal acceleration we just calculated.
Force = 25.0 kg * 1.52 m/s^2 = 38 N.
Therefore, the net horizontal force exerted on the child is 38 Newtons.