A 70.50 kg man rides a Ferris wheel with a radius of 10.3 m at a velocity of 5.00 m/s. What is the centripetal force that she experiences expressed with the correct number of significant figures?
171 N
The net force that produces centripetal motion is
M V^2/R. Compute it and round the answer to three significant figures.
To find the centripetal force experienced by the man on the Ferris wheel, we can use the formula:
F = m * a
Where F is the force, m is the mass, and a is the centripetal acceleration.
The centripetal acceleration can be calculated using the formula:
a = v^2 / r
Where v is the velocity and r is the radius.
Substituting the given values:
v = 5.00 m/s
r = 10.3 m
a = (5.00 m/s)^2 / 10.3 m
= 25.00 m^2/s^2 / 10.3 m
≈ 2.43 m/s^2
Now we can calculate the force:
F = m * a
= 70.50 kg * 2.43 m/s^2
≈ 171.0 N
Therefore, the centripetal force experienced by the man is approximately 171.0 N.
To calculate the centripetal force experienced by the man riding the Ferris wheel, we can use the formula:
F = m * (v^2 / r)
Where:
F is the centripetal force
m is the mass of the man (70.50 kg)
v is the velocity of the man (5.00 m/s)
r is the radius of the Ferris wheel (10.3 m)
Now let's substitute the given values into the formula and solve for F:
F = 70.50 kg * (5.00 m/s)^2 / 10.3 m
First, let's calculate v^2:
v^2 = 5.00 m/s * 5.00 m/s = 25.00 m^2/s^2
Now, let's calculate F:
F = 70.50 kg * 25.00 m^2/s^2 / 10.3 m
F = 1662.50 kg * m / s^2 / 10.3 m
F = 161.165 m * kg / s^2
Now, let's express the answer with the correct number of significant figures. The given mass has 4 significant figures, and the given radius has 3 significant figures. Since the centripetal force is calculated using multiplication and division, the result should be rounded to the least number of significant figures (which is 3 in this case):
F = 161 m * kg / s^2
So, the centripetal force experienced by the man riding the Ferris wheel is approximately 161 newtons (N), with the correct number of significant figures.