A car with a mass of 1,500 kilograms is moving around a circular curve at a uniform velocity of 16 m/s. The curve has a radius of 100 meters. What's the centripetal force on the car?

Respuesta :

Centripetal force can be computed using this formula.

[tex]f = \frac{mv^{2} }{r} [/tex]

where:
f= centripetal force
m = mass
v = velocity
r = radius

Everything you need is already and all you have to do is input it into your formula:
m = 1,500 kg
v = 16m/s
r = 100  m

[tex]f = \frac{(1,500kg)(16m/s)^{2} }{100m} [/tex]
[tex]f = \frac{1,500kg)(256m^{2}/s^{2}) }{100m} [/tex]
[tex]f = \frac{384,000kg.m^{2}/s^{2} }{100m} [/tex]
[tex]f = 3,840 kg.m/s^{2}[/tex] or [tex]f = 3,840 N[/tex]

The centripetal force in a circular motion is given by:
[tex]F_C = m \frac{v^2}{r} [/tex]
where m is the mass of the object, v its speed and r the radius of the circular path.
Using the data of this problem, m=1500 kg, v=16 m/s and r=100 m, and replacing them inside the formula, we find the value of the centripetal force:
[tex]F_C = (1500 kg) \frac{(16 m/s)^2}{100 m}=3840 N [/tex]