Linc, the 65kg lifeguard, slides down a water slide that is inclined at an angle of 35 degrees to the horizontal, into the community swimming pool. If the coefficient of friction of the slide is 0.050, what is Linc's rate of acceleration as he slides down?
-Draw the free body diagram for this problem, be sure to include: weight(which you need to solve for), normal force, the resultant that his movement will follow, the angle of the slide, friction, and any other important information. BE SURE TO LABEL YOUR ARROWS! You do NOT need to solve for Linc's acceleration.
5.2
To find Linc's rate of acceleration as he slides down the water slide, we need to analyze the forces acting on him.
First, let's draw the free body diagram for this problem:
1. Start by drawing a downward arrow labeled "Weight" to represent Linc's weight. The weight is given as 65 kg, so we can calculate it using the equation: Weight = mass x gravity. The acceleration due to gravity is approximately 9.8 m/s^2, so the weight would be 65 kg x 9.8 m/s^2.
2. Draw an arrow perpendicular to the surface of the slide and labeled "Normal force." The normal force is the force exerted by the slide to prevent Linc from sinking through the slide. It acts perpendicular to the surface, so it counteracts a component of Linc's weight.
3. Draw an arrow pointing parallel to the inclined slide and labeled "Resultant force." This force represents the direction of Linc's movement, parallel to the slide. We want to find his acceleration in this direction.
4. Draw an arrow pointing in the opposite direction of the resultant force, labeled "Friction." Friction opposes the direction of motion and is proportional to the normal force. We can calculate the friction force using the equation: Friction = coefficient of friction * normal force.
5. Label the angle of the slide as 35 degrees.
By looking at this diagram, we can determine the forces acting on Linc and how they relate to each other. To actually solve for Linc's acceleration, we'll need more information such as the slope length of the slide or any external forces acting on him.
To determine Linc's rate of acceleration as he slides down the water slide, we need to construct a free body diagram that includes all the relevant forces acting on him. Here's how:
1. First, let's draw a horizontal line to represent the ground or the reference point. Then, draw a vertical line perpendicular to the ground to represent the water slide.
2. Label Linc's weight as "W" pointing downward, which can be calculated using the equation W = mass × gravitational acceleration. In this case, W = 65 kg × 9.8 m/s².
3. Draw a normal force perpendicular to the water slide and label it as "N." This force opposes the weight and acts perpendicularly to the water slide.
4. Next, draw a dotted line parallel to the water slide, which represents the resultant of the weight and the normal force. Label this line as "R" to represent the net force acting on Linc parallel to the incline.
5. Draw a horizontal line pointing downhill and label it as "Ff" for the force of friction. This force acts to oppose Linc's motion down the water slide. Its value can be calculated by multiplying the coefficient of friction (0.050) by the normal force.
6. Finally, label the angle of the slide as 35 degrees. This angle is measured between the ramp and the reference line (ground).
By constructing this free body diagram, we can now analyze the forces acting on Linc and determine his rate of acceleration.