A 3.1 kg block has an initial velocity of 15 m/s as it moves 12m on a rough horizontal surface with coefficient of kinetic friction of .23.. ~ then slides up a frictionless incline whose angle is 24 degrees.
A (8 pts) Sketch energy pie charts at points a, band c. (Point c is the maximum height) Be sure to get changes correct. That is, if kinetic energy increases between two points, make that clear. But you won't be able to get the fractions of energy correct at this point.
B. (16 pts) Find how high the block goes up the hill. Be sur~ to, check your units explicitly and show the details of simplification.
What is your question about this?
How high does the block go up?
initial KE-frictionwork=change in GPE
1/2 m*15^2-mu*mg*cosTheta*12=
=mgh where h is the vertical height it goes up vertically. the distance along the plane will be h/sinTheta
To sketch the energy pie charts at points a, b, and c, we need to understand the different forms of energy involved and their changes at each point.
At point a (initial position on the rough horizontal surface):
- The only form of energy present is kinetic energy (KE) due to the block's initial velocity.
At point b (end of the rough horizontal surface/start of the incline):
- The block is moving up the incline, so it gains potential energy (PE) as it moves against gravity.
- Some of the block's initial kinetic energy is converted to work against friction, resulting in a decrease in kinetic energy.
At point c (maximum height on the incline):
- The block has stopped moving, so its kinetic energy is zero.
- The block's potential energy is now at its maximum since it has reached the highest point on the incline.
Now, let's calculate the height the block reaches (part B):
Step 1: Find the work done by friction on the rough horizontal surface.
- The work done by friction is given by the equation: work = force × distance × cos(theta), where theta is the angle between the force and the displacement.
- The force of friction is given by the equation: force = coefficient of kinetic friction × normal force.
- The normal force is equal to the block's weight (mass × gravity).
- Therefore, the work done by friction = (coefficient of kinetic friction × mass × gravity) × distance.
- Substitute the given values: work = (0.23 × 3.1 kg × 9.8 m/s^2) × 12 m.
Step 2: Calculate the change in mechanical energy between points a and b.
- The change in mechanical energy = work done by friction.
- Substitute the previously calculated work value.
Step 3: Calculate the height the block reaches on the incline.
- The change in mechanical energy between point b and point c is equal to the change in potential energy (PE) at point c.
- The change in potential energy = mass × gravity × height.
- Convert the change in mechanical energy (Joules) to potential energy (Joules) by multiplying by -1 since we are considering the decrease in mechanical energy.
- Substitute the given values: (mass × gravity × height) = -change in mechanical energy.
- Rearrange the equation and solve for height.
Make sure to plug in the appropriate calculations and units to get the final answer for the height the block reaches on the incline.