Distance Block Slides Up Ramp

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In summary, the problem involves a block with a mass of 2.96 kg sliding up a ramp with an initial speed of 12.8 m/s. The ramp is inclined at an angle of 36.4 degrees and has a coefficient of kinetic friction of 0.45. The goal is to find the displacement of the block along the ramp until it stops. The equations used include work-energy theorem, work integral, and initial and final kinetic energies. The correct method involves including the gravitational potential energy in the calculation.
  • #1
getty102
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Homework Statement


A block of mass 2.96 kg is sliding up a ramp with an initial speed of 12.8 m/s. The ramp is inclined from the horizontal at an angle of 36.4 degrees and the coefficient of kinetic friction is [itex]\mu[/itex]=045. What is the displacement of the block along the ramp from the initial time until it stops?


Homework Equations



W=ΔE
W=∫F*ds
ΔE=(m/2)(vf)2-(m/2)(v0)2 where (vf)=0
[itex]\Phi[/itex]=36.4
m=2.96kg
v0=12.8 m/s
[itex]\mu[/itex]= 0.45

The Attempt at a Solution



[itex]\mu[/itex]*m*g*cos[itex]\Phi[/itex]x=-(m/2)(v0)2
solve for x
x=-(m/2)(v0)2/[itex]\mu[/itex]*m*g*cos[itex]\Phi[/itex]
 
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  • #2
hi getty102! :smile:

correct method, but you forgot to include the gravitational PE (or gravitational work done) :wink:
 
  • #3
Cool, thank you. The potential energy from gravity is dependent on the height. Which in this problem is kind of what I'm looking for because if I can find the height I would know the total displacement of the block up the ramp.
 
  • #4
xsinΦ ? :wink:
 
  • #5


I would first like to clarify that the given problem statement does not provide enough information to accurately solve for the displacement of the block along the ramp. The equation provided in the "Attempt at a Solution" section is incorrect as it does not take into account the work done by the friction force. In addition, the direction of the displacement is not specified in the problem statement, which could also affect the calculation.

Assuming that the displacement is in the direction of motion of the block, the correct equation to use would be:

W = ΔE = ΔK + ΔU + ΔWfr

Where ΔK is the change in kinetic energy, ΔU is the change in potential energy, and ΔWfr is the work done by the friction force. Using the given information, we can calculate the work done by the friction force as:

ΔWfr = -μmgcosΦx

Where x is the displacement along the ramp. The work-energy theorem states that the work done by all forces is equal to the change in kinetic energy, so we can set up the following equation:

ΔK = ΔWfr

Substituting in the values, we get:

(m/2)(vf)^2 - (m/2)(v0)^2 = -μmgcosΦx

Since the final velocity of the block is 0, we can solve for x:

x = (v0^2/2μgcosΦ)

Plugging in the given values, we get a displacement of approximately 7.85 meters. However, it is important to note that this calculation assumes that the block is sliding up the ramp without any external force acting on it. If there are other forces involved, such as an applied force, the calculation would be different. Additionally, the direction of the displacement may also change depending on the specific problem scenario.
 

1. What is a distance block slide up ramp experiment?

A distance block slide up ramp experiment is a scientific investigation that involves measuring the distance a block travels up a ramp when released from different starting points. This experiment is used to study the relationship between the height of the ramp and the distance the block travels, as well as the effects of other variables such as the angle of the ramp, the weight of the block, and the surface of the ramp.

2. What materials are needed for a distance block slide up ramp experiment?

The materials needed for a distance block slide up ramp experiment include a ramp, a block, a measuring tool, a stopwatch, and a surface to set up the experiment on. The ramp can be made of any sturdy material, such as wood or cardboard, and the block can be any shape or size as long as it can slide smoothly up the ramp. It is also helpful to have a protractor to measure the angle of the ramp.

3. How do you set up a distance block slide up ramp experiment?

To set up a distance block slide up ramp experiment, place the ramp on a flat surface and adjust the angle of the ramp using a protractor. Place the block at the bottom of the ramp and choose a starting point for the block to be released from. Use a measuring tool to mark the distance the block travels up the ramp from the starting point. Repeat this process for different starting points and record the distance traveled each time.

4. What factors can affect the distance a block travels up a ramp?

The distance a block travels up a ramp can be affected by various factors, including the angle of the ramp, the weight of the block, the surface of the ramp, and the starting point of the block. A steeper ramp will result in a shorter distance traveled, while a lighter block will travel a longer distance. The surface of the ramp can also affect the block's speed and distance traveled. Additionally, the starting point can impact the force and velocity of the block as it moves up the ramp.

5. What can be learned from a distance block slide up ramp experiment?

A distance block slide up ramp experiment can teach us about the relationship between height and distance, as well as the effects of other variables on the distance a block travels. It can also help us understand concepts such as force, velocity, and acceleration. This experiment can also be used to make predictions and test hypotheses about the factors that affect the motion of objects on inclined surfaces.

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