Question

A child with a mass of 30 kg slides down a slide at an angle of 40º from the horizontal. She accelerates at 1.3 m/s2. Calculate the magnitude of the frictional force on the child.

Answer 1

Here Solved :

Step-by-step explanation:

horizontal component of acceleration due to gravity is balanced by centrifugal force and the net force acting on a body that will ma and hence

Mgsin40 - Frictional force = Ma

Answer 2

150 N.

Step-by-step explanation:

Here are the steps on how to calculate the magnitude of the frictional force on the child:

1. Identify the known and unknown quantities.

Given:

* Mass of the child, m = 30 kg

* Angle of the slide, θ = 40°

* Acceleration of the child, a = 1.3 m/s2

Unknown:

* Magnitude of the frictional force, Ff

2. Draw a free-body diagram of the child.

A free-body diagram is a diagram that shows all the forces acting on an object. In this case, the forces acting on the child are the force of gravity, the normal force, and the frictional force. Attachment

3. Apply Newton's second law to the child.

Newton's second law states that the net force acting on an object is equal to the mass of the object times its acceleration. In this case, the net force is the difference between the force of gravity and the frictional force.

Fnet = mg Sin(∅) - Ff

4. Substitute the known values into the equation.

mgSin(∅) - Ff = ma

(30 kg)(9.8 m/s^2) Sin40º-Ff = (30 kg)(1.3 m/s^2)

189 N -Ff = -39 N

5. Solve for the magnitude of the frictional force.

Ff = -39 N-189 N

|Ff| = 150 N

Therefore, the magnitude of the frictional force on the child is 150 N.

The frictional force is acting in the opposite direction of the child's motion, so it is slowing her down.