a toy car moves around a loop-the-loop truck. the loop is 0.5m high what is the minimum speed of the car at the top of the loop for it to stay on track?
To determine the minimum speed of the toy car at the top of the loop for it to stay on track, we can use the concept of centripetal force.
First, let's consider the forces acting on the car at the top of the loop. There are two forces involved:
1. Gravitational force (mg) acting vertically downwards.
2. Centripetal force (Fc) acting towards the center of the loop.
At the top of the loop, the car needs to maintain contact with the track, so the centripetal force must be equal to or greater than the gravitational force.
Step 1: Calculate the gravitational force:
The gravitational force is given by the formula: Fg = mg, where m is the mass of the car and g is the acceleration due to gravity (approximately 9.8 m/s²).
Step 2: Calculate the centripetal force:
The centripetal force is given by the formula: Fc = (mv²) / r, where m is the mass of the car, v is the velocity of the car, and r is the radius of the loop.
In this case, the radius of the loop can be considered as the height of the loop (0.5 m).
Step 3: Equate the forces:
Setting Fc ≥ Fg,
(mv²) / r ≥ mg.
Step 4: Solve for the minimum speed:
Rearranging the equation,
v² ≥ rg.
Now, substitute the known values:
v² ≥ (0.5 m) * (9.8 m/s²).
v² ≥ 4.9 m²/s².
Finally, taking the square root of both sides, we find:
v ≥ √(4.9 m²/s²).
Therefore, the minimum speed of the car at the top of the loop for it to stay on track is approximately 2.21 m/s.