Determine the tangential and centripetal components of the net force exerted on a car (by the ground) when its speed is 30 m/s , and it has accelerated to this speed from rest in 8.5 s on a curve of radius 500 m . The car's mass is 1200 kg
To determine the tangential and centripetal components of the net force exerted on the car, we need to understand the forces acting on the car and use the concepts of centripetal force and tangential acceleration.
1. Find the centripetal force:
The centripetal force is the force that keeps an object moving in a circular path. It is given by the equation:
F_c = (m * v^2) / r
where:
- F_c is the centripetal force
- m is the mass of the car (1200 kg)
- v is the velocity of the car (30 m/s)
- r is the radius of the curve (500 m)
Plugging in the values, we get:
F_c = (1200 kg * (30 m/s)^2) / 500 m
F_c = 21,600 N
2. Find the tangential force:
The tangential force is the force responsible for the change in speed of the car. In this case, the car starts from rest and accelerates to a speed of 30 m/s in 8.5 s. We can use Newton's second law of motion to find the tangential force:
F_t = m * a_t
where:
- F_t is the tangential force
- m is the mass of the car (1200 kg)
- a_t is the tangential acceleration
To find the tangential acceleration, we can use the formula:
a_t = (v - v0) / t
where:
- v is the final velocity (30 m/s)
- v0 is the initial velocity (0 m/s)
- t is the time taken to reach the final velocity (8.5 s)
Plugging in the values, we get:
a_t = (30 m/s - 0 m/s) / 8.5 s
a_t = 3.53 m/s^2
Now, we can find the tangential force:
F_t = 1200 kg * 3.53 m/s^2
F_t = 4,236 N
3. Determine the net force components:
The net force can be divided into two components: the centripetal component (F_c) and the tangential component (F_t). Since these two forces act at right angles to each other, we can use vector addition to find the net force.
Net force = sqrt(F_c^2 + F_t^2)
Plugging in the values, we get:
Net force = sqrt((21,600 N)^2 + (4,236 N)^2)
Net force ≈ 21,964 N
Therefore, the tangential force is approximately 4,236 N, and the centripetal force is approximately 21,600 N.