A car is travelling on a circular hill. If the car is travelling at 11.1 m/sec, what is the car's centripetal acceleration? If the car weighs 1200 kg, what net force would be needed to cause this centripetal acceleration? Find the maximum velocity that the car can travel without flying off the hill
First, we can calculate the centripetal acceleration using the formula. This formula was derived based on the fact that the only things affecting the object's acceleration are the car's tangential velocity and the radius of curvature. Since we know both, we can input them into the equation to solve for centripetal acceleration.
Ac = V^2/r
Ac = (11.1)^2/ 25
Ac = 4.93 m/sec^2
Ac = (11.1)^2/ 25
Ac = 4.93 m/sec^2
To answer the next question, we can use Newton's 2nd Law. Since we know the mass and the centripetal acceleration, we can calculate the net force on the car.
ΣF = m*a
ΣF = 1200 kg *4.93 m/sec^2
ΣF = 5916N
ΣF = 1200 kg *4.93 m/sec^2
ΣF = 5916N
This is the net force on the car. With this, we can draw a force diagram for the car. First, however, we must calculate what force gravity exerts on the car (Wec).
Wec = m*a
Wec = 1200kg 9.8 m/sec^2
Wec = 11760N
The only forces acting upon the car are the weight force and the normal force. We know both the net force and the weight force, so we can solve for the normal (symbolized by Nhc). The net force is downward and the normal force is upward, so they oppose each other. Since the weight force is opposed by the normal force, we must subtract the normal force from the weight force.
ΣF = Wec - Nhc
5916N = 11760N - Nhc
Nhc = 5844N
So, we can draw the force diagram for the car. Because there is acceleration, we know that the forces are unbalanced.
Wec = m*a
Wec = 1200kg 9.8 m/sec^2
Wec = 11760N
The only forces acting upon the car are the weight force and the normal force. We know both the net force and the weight force, so we can solve for the normal (symbolized by Nhc). The net force is downward and the normal force is upward, so they oppose each other. Since the weight force is opposed by the normal force, we must subtract the normal force from the weight force.
ΣF = Wec - Nhc
5916N = 11760N - Nhc
Nhc = 5844N
So, we can draw the force diagram for the car. Because there is acceleration, we know that the forces are unbalanced.
To find the maximum speed, we need to reconsider the force diagram. At the maximum speed possible, the centripetal force would have to equal the weight force. If the centripetal force exceeded the weight force, the car would fly off of the road.
11760N = 1200 kg * (V^2/ r)
V^2/ 25 = 11760/ 1200
V = 15.65 m/sec
V^2/ 25 = 11760/ 1200
V = 15.65 m/sec
The maximum speed the car can go without flying off the hill is 15.65 m/sec.