net force of gravity of child down the slide: force=mgSin38-mg(.162)cos38
finalKEnergy=InitialKE+initial PE - work friction
1/2 m vf^2=1/2 m(.208^2)+mg*5.98*sin38-mg(.162)cos38
solve for vf.
A child slides down a 5.98 m playground slide that makes an angle of 38.0° with the horizontal. The coefficient of kinetic friction between the slide and the child is 0.162. If she starts at the top with a speed of 0.208 m/s, what is her speed (in m/s) at the bottom?
3 answers
This question is hard to solve without a diagram.
Draw a line of approximately 38° above the horizontal, so that it represents the slide. Next, draw a vertical arrow with its tail connected to the angled line about halfway down to represent the child’s weight (mg). Where the arrow and the angled line meet, draw a second arrow with its tail connected to the intersection and perpendicular to the angled line. This second arrow represents the normal force. A third arrow to represent the force of friction is pointing upwards along the slide.
To make it easier to solve, we are going to turn our usual x and y axes at an angle to match the slide. y is going to be in the direction of the normal force and x is going to point along the slide.
Resolve the the force of gravity (mg) into its components using these axes. You don't know "m" so just leave it as m. e.g. force of gravity is 9.8m It will cancel out later
Use the "y" component of gravity as the normal force to find friction.
Use the "x" component of gravity and the frictional force to find the net force. Now you can cancel out m and you are left with a value for acceleration. The rest is a kinematics problem.
Draw a line of approximately 38° above the horizontal, so that it represents the slide. Next, draw a vertical arrow with its tail connected to the angled line about halfway down to represent the child’s weight (mg). Where the arrow and the angled line meet, draw a second arrow with its tail connected to the intersection and perpendicular to the angled line. This second arrow represents the normal force. A third arrow to represent the force of friction is pointing upwards along the slide.
To make it easier to solve, we are going to turn our usual x and y axes at an angle to match the slide. y is going to be in the direction of the normal force and x is going to point along the slide.
Resolve the the force of gravity (mg) into its components using these axes. You don't know "m" so just leave it as m. e.g. force of gravity is 9.8m It will cancel out later
Use the "y" component of gravity as the normal force to find friction.
Use the "x" component of gravity and the frictional force to find the net force. Now you can cancel out m and you are left with a value for acceleration. The rest is a kinematics problem.
Sorry, I was typing up an answer and didn't see that there was already a response.
1 answer