A motorcycle has a mass of 250kg. It goes around a 13.7 m radius turn at 96.5 km/hr. What is the centripetal force?
a. 2.95x10^3 N
b. 4.31x10^4N
c. 1.31x10^4 N
d. 719N
change velocity in km/hr to m/s
force= m v^2/r
To find the centripetal force, we can use the formula:
F = (m * v^2) / r
where:
F is the centripetal force,
m is the mass of the motorcycle,
v is the velocity of the motorcycle, and
r is the radius of the turn.
Given:
m = 250 kg,
v = 96.5 km/hr = 26.8 m/s (since 1 km/hr = 1 m/s),
r = 13.7 m.
Now, we can substitute the values into the formula:
F = (250 kg * (26.8 m/s)^2) / 13.7 m
Calculating this expression:
F = (250 kg * 718.24 m^2/s^2) / 13.7 m
F = 179,560 N / 13.7 m
F = 13,116.788321167883 N
Rounding this value to three significant figures, the centripetal force is approximately equal to 1.31×10³ N.
Therefore, the correct answer is option c. 1.31×10³ N.
To find the centripetal force of a motorcycle going around a turn, we can use the formula:
F = (m * v^2) / r
where F is the centripetal force, m is the mass of the motorcycle, v is the velocity, and r is the radius of the turn.
First, let's convert the velocity from km/hr to m/s. To do this, divide the velocity by 3.6:
96.5 km/hr / 3.6 = 26.81 m/s
Now we have the velocity (v = 26.81 m/s), the radius (r = 13.7 m), and the mass (m = 250 kg).
Plug these values into the formula:
F = (250 kg * (26.81 m/s)^2) / 13.7 m
Calculating:
F = (250 kg * 719.76 m^2/s^2) / 13.7 m
F = 179,940 N / 13.7
F = 13,132.12 N
Rounding to the appropriate number of significant figures, we get:
F ≈ 1.31 × 10^4 N
Therefore, the correct answer is option c. 1.31 × 10^4 N.