At a playground, a child slides down a slide that makes a 42° angle with the horizontal direction. The coefficient of kinetic friction for the child sliding on the slide is 0.20. What is the magnitude of her acceleration during her sliding? A)4.6 m/s² B)5.1 m/s² C)5.4 m/s² D)6.3 m/s² E)9.8 m/s²

Question

Quizplus · Accepted Answer

First we need to find the component of the gravitational force parallel to the slide. This can be computed using:

F_parallel = m*g*sin(42°)

where m is the mass of the child and g is the acceleration due to gravity.

Next, we need to find the frictional force acting on the child as she slides down. This can be computed using:

F_friction = μ*m*g*cos(42°)

where μ is the coefficient of kinetic friction.

The net force acting on the child down the slide is:

F_net = F_parallel - F_friction

The acceleration of the child is given by:

a = F_net / m

Substituting the expressions for F_parallel and F_friction, we get:

a = (m*g*sin(42°) - μ*m*g*cos(42°)) / m

Simplifying, we get:

a = g*(sin(42°) - μ*cos(42°))
a = 5.1 m/s^2

Therefore, the magnitude of the child's acceleration during her sliding is 5.1 m/s^2.

At a Playground, a Child Slides Down a Slide That