A person drives a car around a circular cloverleaf with a radius of 58 m at a uniform speed of 10 m/s. ) Compare this answer with the acceleration due to gravity as a percentage
Centripetal acceleration
a=v²/R=10²/58 = 1.72 m/s²
9.8 ....100%
1.72.....x%
x=1.72•100/9.8 =17.6%
A person drives a car around a circular cloverleaf with a radius of 78 m at a uniform speed of 9 m/s.
(a) What is the acceleration of the car?
(b) Compare the answer with the acceleration due to gravity as a percentage.
To compare the answer with the acceleration due to gravity as a percentage, we first need to calculate the acceleration of the car as it moves in a circular path.
The acceleration of an object moving in a circle is given by the formula:
a = v^2 / r
Where:
a = acceleration
v = speed or velocity
r = radius of the circular path
In this case, the speed of the car is 10 m/s and the radius of the circular cloverleaf is 58 m. Plugging in these values, we can calculate the acceleration:
a = (10 m/s)^2 / 58 m
a ≈ 17.241 m/s^2
Now, let's compare this acceleration with the acceleration due to gravity, which is approximately 9.8 m/s^2.
To calculate the percentage, we can use the formula:
Percentage = (a / g) * 100
where g is the acceleration due to gravity.
Percentage = (17.241 m/s^2 / 9.8 m/s^2) * 100
Percentage ≈ 176.032 %
Therefore, the acceleration of the car driving around the circular cloverleaf is approximately 176.032% of the acceleration due to gravity.
To compare the answer with the acceleration due to gravity as a percentage, we first need to determine the car's acceleration as it moves around the circular cloverleaf.
The acceleration of an object moving in a circle can be calculated using the equation:
a = (v^2) / r,
where a is the acceleration, v is the velocity, and r is the radius of the circle.
In this case, the velocity (v) is given as 10 m/s, and the radius (r) is given as 58 m.
Plugging these values into the equation, we get:
a = (10^2) / 58
a = 100 / 58
a ≈ 1.7241 m/s^2
Now, let's compare this value with the acceleration due to gravity (denoted as 'g'). On Earth, the approximate value of acceleration due to gravity is 9.8 m/s^2.
To calculate the percentage, we can use the formula:
percentage = (a / g) * 100
Plugging in the values, we find:
percentage = (1.7241 / 9.8) * 100
percentage ≈ 17.6%
Therefore, the car's acceleration while driving around the circular cloverleaf at a uniform speed of 10 m/s is approximately 17.6% of the acceleration due to gravity.