(I) determine the tangential and centripetal components of the net force excreted on the car(by the ground) when it accelerates at a uniform speed of 15 m/s in 11 s, moving on a circular track of radius 500m. The cars mass is 1100kg.
To determine the tangential and centripetal components of the net force exerted on the car when it accelerates on a circular track, we need to use the following formulas:
1. Net Force (F_net) = mass (m) × acceleration (a)
2. Tangential Force (F_tan) = mass (m) × tangential acceleration (a_tan)
3. Centripetal Force (F_c) = mass (m) × centripetal acceleration (a_c)
First, we need to calculate the tangential acceleration. The car is moving at a uniform speed, so the tangential acceleration is zero.
Next, we need to calculate the centripetal acceleration using the formula:
Centripetal acceleration (a_c) = (tangential speed)^2 / radius
Given that the tangential speed is 15 m/s and the radius is 500 m, we substitute these values into the formula:
a_c = (15 m/s)^2 / 500 m = 0.45 m/s^2
Now, we can find the net force exerted on the car by substituting the values of acceleration and mass into the formula:
F_net = m × a
F_net = 1100 kg × 0.45 m/s^2 = 495 N
Since the tangential acceleration is zero, the tangential force on the car is also zero:
F_tan = m × a_tan
F_tan = 1100 kg × 0 m/s^2 = 0 N
Finally, the centripetal force is equal to the net force:
F_c = F_net
F_c = 495 N
To summarize:
- The tangential component of the net force exerted on the car (by the ground) is 0 N.
- The centripetal component of the net force exerted on the car (by the ground) is 495 N.