A 0.5 kg ball whirls on a string at a steady 4 m/s, around a circle of radius 2 m.
How big is the centripetal force on it? And when the force is the known thing, how do you find the mass, or the radius?
Start with the ball's own numbers: m = 0.5 kg, v = 4 m/s, r = 2 m.
Multiply the mass by the squared speed, and divide by the radius: (0.5 × 4 × 4) / 2 = 4. The centripetal force on the ball is 4 N.
That move is the equation you have seen: F = mv²/r.
Step 1: write down the values in the question, and mark the unknown.
Step 2: write down the equation. If the unknown is m or r, make it the subject first: m = Fr/v², or r = mv²/F.
Step 3: substitute in the values, and calculate. The result line carries its unit.
Finding the speed v from the others needs a square root; that direction is its own lesson. Here the unknown is F, m, or r.
A 0.5 kg ball whirls on a string at a steady 4 m/s, around a circle of radius 2 m. Calculate the centripetal force on it.
Write down the values:
m = 0.5 kg, v = 4 m/s, r = 2 m, F = ?
Write down the equation:
F = mv²/r
Substitute in the values, and calculate:
F = (0.5 × 4 × 4) / 2 = 4
The centripetal force on the ball is 4 N.
A cart circles a flat loop of radius 9 m at a steady 6 m/s. The net inward force on it is 32 N. Calculate its mass.
Write down the values:
F = 32 N, v = 6 m/s, r = 9 m, m = ?
Make m the subject:
m = Fr/v²
Substitute in the values, and calculate:
m = (32 × 9) / (6 × 6) = 8
The cart's mass is 8 kg.
A 3 kg skateboard is towed in a circle of radius 25 m at a steady 10 m/s by a rope staked at the center. Enter the rope's inward force on it in N.
A 1.2 kg ball on a cord circles at a steady 5 m/s on a circle of radius 2 m. Enter the centripetal force on it in N.
A child rides a merry-go-round of radius 7 m at a steady 3 m/s. The net inward force on the child is 54 N. Enter the child's mass in kg.
A 5 kg crate rides a rotating platform at a steady 6 m/s, held by a 25 N inward friction force. Enter the radius of its circle in m.
A sled is towed in a circle of radius 30 m on smooth ice at a steady 10 m/s. The rope's inward force on it is 60 N. Enter the sled's mass in kg.
A 2 kg exercise ball on a 3.5 m cord is swung in a horizontal circle. Its speed holds steady at 7 m/s. Enter the cord's inward force on it in N.
A 2.2 kg puck on a cord circles a peg on smooth ice, radius 2.5 m, at a steady 5 m/s. Enter the cord's inward force on it in N.
A 4 kg training ball is swung on a short rope in a horizontal circle at a steady 5 m/s. The rope supplies an 80 N inward force. Enter the circle's radius in m.
A motorcycle and its rider take a flat circular test loop of radius 120 m, holding a steady 20 m/s the whole way around. The track supplies a 600 N inward force on them. Enter their combined mass in kg.