A train whose speed is 100km/hr rounds a curve whose radius of curvature is 150m what is the acceleration?
5.4 m/s^2
To find the acceleration of the train rounding the curve, we can use the centripetal acceleration formula. Centripetal acceleration is given by the equation:
a = v² / r
where:
a = acceleration
v = velocity (speed) of the train
r = radius of curvature
In this case,
v = 100 km/hr = (100 * 1000) m/3600 s (converting km/hr to m/s)
v = 27.78 m/s (approx.)
r = 150 m
Using the formula, we can find the acceleration:
a = (27.78 m/s)² / 150 m
a ≈ 5.13 m/s²
Therefore, the acceleration of the train rounding the curve is approximately 5.13 m/s².
To calculate the acceleration of the train rounding the curve, we need to use the centripetal acceleration formula. The centripetal acceleration is the acceleration experienced by an object moving in a circle.
The formula for centripetal acceleration is given by:
a = v^2 / r
where:
a = centripetal acceleration
v = velocity of the object
r = radius of the curve
First, we need to convert the speed of the train from km/hr to m/s. Since 1 km = 1000 m and 1 hour = 3600 s, we can convert the units as follows:
100 km/hr * (1000 m / 1 km) * (1 hr / 3600 s) = 27.78 m/s
Now that we have the velocity, we can substitute the values into the formula:
a = (27.78 m/s)^2 / 150 m
Simplifying the equation, we get:
a = 771.16 m^2/s^2 / 150 m
Now, divide the numerator by the denominator to obtain the acceleration:
a = 5.14 m/s^2
Therefore, the acceleration of the train rounding the curve is 5.14 m/s^2.