A 51kg person on a merry-go-round is traveling in a circle with a radius of 2 m at a speed of 6 m/s

A) What acceleration does the person experience?
B) What is the net horizontal force?
C) How does it compare with the person's weight?

Ac = v^2/r = 36/2 = 18 m/s^2

m
F = M Ac = 51 *18 Newtons

weight = 51 * 9.81 Newtons

almost 2 g

acceleration= v^2/r

force=mass*acceleration
weight=51*9.8 N

To determine the acceleration experienced by the person on the merry-go-round, we can use the formula for centripetal acceleration:

a = v^2 / r

where:
a = acceleration
v = velocity
r = radius

Given that the person is traveling in a circle with a radius of 2 m at a speed of 6 m/s, we can substitute these values into the formula:

a = (6 m/s)^2 / 2 m
a = 36 m^2/s^2 / 2 m
a = 18 m/s^2

Therefore, the person experiences an acceleration of 18 m/s^2.

To find the net horizontal force acting on the person, we can use Newton's second law of motion:

F = m × a

where:
F = force
m = mass
a = acceleration

Given that the mass of the person is 51 kg and the acceleration is 18 m/s^2, we can substitute these values into the equation:

F = 51 kg × 18 m/s^2
F = 918 N

Therefore, the net horizontal force acting on the person is 918 N.

To compare this force with the person's weight, we need to calculate the weight of the person. The weight can be calculated using the formula:

Weight = mass × gravitational acceleration

where the gravitational acceleration is approximately 9.8 m/s^2.

Weight = 51 kg × 9.8 m/s^2
Weight = 499.8 N

Comparing the net horizontal force (918 N) with the person's weight (499.8 N), we can see that the force is greater than the person's weight.

To answer these questions, we'll need to understand the concept of centripetal acceleration, centripetal force, and Newton's second law of motion.

A) The centripetal acceleration is given by the formula:

ac = v^2 / r

where:
ac is the centripetal acceleration,
v is the linear velocity,
and r is the radius of the circle.

Using the given values:
v = 6 m/s
r = 2 m

Substituting these values into the formula, we have:

ac = (6 m/s)^2 / 2 m
ac = 36 m^2/s^2 / 2 m
ac = 18 m/s^2

So, the person experiences a centripetal acceleration of 18 m/s^2.

B) The net horizontal force acting on the person is the centripetal force, which is given by the formula:

Fc = m * ac

where:
Fc is the centripetal force,
m is the mass of the person,
and ac is the centripetal acceleration.

Using the given value:
m = 51 kg

Substituting this value along with the previously calculated centripetal acceleration (ac = 18 m/s^2), we have:

Fc = 51 kg * 18 m/s^2
Fc = 918 N

So, the net horizontal force acting on the person is 918 Newtons.

C) Now, to compare the net horizontal force with the person's weight, we need to calculate the weight of the person.

The weight of an object can be calculated using the formula:

w = m * g

where:
w is the weight,
m is the mass of the object,
and g is the acceleration due to gravity.

The typical value for g is approximately 9.8 m/s^2.

Using the given value for the person's mass (m = 51 kg) and the acceleration due to gravity (g = 9.8 m/s^2), we have:

w = 51 kg * 9.8 m/s^2
w = 499.8 N

So, the person's weight is approximately 499.8 Newtons.

Comparing the net horizontal force (Fc = 918 N) with the person's weight (w = 499.8 N), we can see that the net horizontal force is greater than the person's weight.