Question3. A child of mass 40.0 kg is in a roller coaster car that travels in a loop of radius 7.00 m . At point $A$ the speed of the car is $10.0 \mathrm{~m} / \mathrm{s}$, and at point $B$, the speed is $10.5 \mathrm{~m} / \mathrm{s}$. Assume the child is not holding on and does not wear a seat belt. (a) What is the force of the car seat on the child at point $A$ ? ( $b$ ) What is the force of the car seat on the child at point $B$ ? (c) What minimum speed is required to keep the child in his seat at point $A$ ?

Studdy Solution
Determine the minimum speed required to keep the child in the seat at point $A$:
At the top of the loop, the minimum speed occurs when the centripetal force equals the gravitational force:
$$\frac{m v^2}{r} = mg$$
$$v^2 = rg$$
$$v = \sqrt{rg}$$
Substitute the given values:
$$v = \sqrt{7.00 \, \text{m} \times 9.81 \, \text{m/s}^2}$$
$$v = \sqrt{68.67}$$
$$v = 8.29 \, \text{m/s}$$
The forces of the car seat on the child are:
(a) At point $A$: $\boxed{179.03 \, \text{N}}$
(b) At point $B$: $\boxed{237.6 \, \text{N}}$
(c) Minimum speed at point $A$: $\boxed{8.29 \, \text{m/s}}$