The free-rolling ramp has a weight of 135 lb The crate whose weight is 72 lb slides from rest at A , 15ft down the ramp to B. The ramps is also at rest when the crate is at A. Assume that the ramp is smooth, and neglect the mass of the wheels.
basicall the picture looks like this:
there's a ramp in a triangle shape with two wheels on bottom.
the crate is sitting on top of triangle which is A. It will slide to B which is at bottom.
the angle can be found out from a 3-4-5 triangle
As the crate (C) travels from point A to point B on the ramp (R). Which of the following statements are true?
Pick all correct answers.
A) The velocity of the crate is at 36.9 from the horizontal.
B)Energy of the crate is conserved.
C)Energy of the ramp is conserved.
D)Energy of the system of (crate+ramp) is conserved.
E)Momentum of the system of (crate+ramp) is conserved in all directions.
F) Momentum of the system of (crate+ramp) is not conserved in all directions, but is conserved in at least one direction
i think it's A, D, and F. am i correct
D and F only
To answer this question, let's go through each statement and determine if it is true or not:
A) The velocity of the crate is at 36.9 from the horizontal.
To find the velocity of the crate at point B, we need to analyze the motion on the ramp. Since the ramp is smooth, there is no friction. The only force acting on the crate is its weight, which can be decomposed into two components: one parallel to the ramp and the other perpendicular to it. Since there is no force parallel to the ramp, the crate will only accelerate in the downward direction. Therefore, the velocity of the crate at point B will not have any horizontal component and will be purely vertical. So statement A is incorrect.
B) Energy of the crate is conserved.
The principle of conservation of energy states that the total mechanical energy (kinetic energy + potential energy) of a system remains constant if no external forces do work on it. In this case, the only force doing work on the crate is its weight, which is converted into kinetic energy. As the crate slides down the ramp, its potential energy decreases, and its kinetic energy increases. Therefore, the energy of the crate is not conserved. So statement B is incorrect.
C) Energy of the ramp is conserved.
Similar to statement B, the energy of the ramp is not conserved. As the crate slides down, the ramp is also experiencing a change in potential energy. So statement C is incorrect.
D) Energy of the system of (crate+ramp) is conserved.
Since both statement B and C are incorrect, it follows that the energy of the system of (crate+ramp) is also not conserved. So statement D is incorrect.
E) Momentum of the system of (crate+ramp) is conserved in all directions.
Momentum is conserved in a closed system when there are no external forces acting on it. In this case, since there is no external force acting on the system of (crate+ramp) other than the weight of the crate, the momentum is conserved in the vertical direction. However, the momentum will not be conserved in the horizontal direction because there is no horizontal force acting on the system. So statement E is incorrect.
F) Momentum of the system of (crate+ramp) is not conserved in all directions but is conserved in at least one direction.
As discussed above, the momentum of the (crate+ramp) system is conserved in the vertical direction but not in the horizontal direction. Therefore, statement F is correct.
Considering the analysis above, the correct statements are F).