A 1200 kg car rounds a flat circular bend of radius 90 m at a steady 15 m/s. You have seen what the needed centripetal force grows with: more mass, more speed, a tighter bend.
How large is the centripetal force the car needs?
You can already get there with tools you have. The car's centripetal acceleration: a = (15 × 15) / 90 = 2.5 m/s².
Newton's second law from the dynamics topic turns that into the needed net force: F = 1200 × 2.5 = 3000 N.
Could one equation do both steps at once? Well, yes: substitute a = v²/r into F = ma, and the second law reads:
F: centripetal force, the net inward force (N) · m: mass (kg) · v: speed (m/s) · r: radius (m).
It is not a new law: F = ma with the circular-motion acceleration substituted in.
The speed is squared. That is why doubling a car's speed quadruples the inward force its tires must supply.
A 1200 kg car rounds a flat circular bend of radius 90 m at a steady 15 m/s. Calculate the centripetal force it needs.
Write down the values:
m = 1200 kg, v = 15 m/s, r = 90 m, F = ?
Write down the equation:
F = mv²/r
Substitute in the values, and calculate:
F = (1200 × 15 × 15) / 90 = 3000
The car needs a centripetal force of 3000 N.
The same car doubles its speed to a steady 30 m/s on the same 90 m bend. Calculate the centripetal force it needs now.
Write down the values:
m = 1200 kg, v = 30 m/s, r = 90 m, F = ?
Write down the equation:
F = mv²/r
Substitute in the values, and calculate:
F = (1200 × 30 × 30) / 90 = 12000
Now the car needs 12000 N, four times the 3000 N from before. Doubling the speed quadrupled the needed force.
A 1.5 kg ball on a cord circles at a steady 6 m/s on a circle of radius 3 m. Enter the centripetal force on it in N.
The centripetal force formula comes from Newton's second law, F = ma. Which substitution for a produces F = mv²/r?
Ines says: because v is squared in F = mv²/r, tripling a cart's speed at a fixed mass and radius makes the needed centripetal force nine times as large. Is she correct?
A 0.6 kg toy plane flies a horizontal circle of radius 5 m on a line, at a steady 10 m/s. Enter the centripetal force on it in N.
Which equation gives the centripetal force needed to hold an object in steady-speed circular motion?
A 900 kg car needs a 1500 N centripetal force to round a flat curve at a steady 10 m/s. It rounds the same curve at a steady 20 m/s. Enter the centripetal force it needs now in N.