Physics Help Greatly Appreciated - Block sliding down ramp

In summary, the conversation discusses the calculation of the time it would take for a 7.7 kg block to slide down a ramp with a coefficient of static friction of 0.50 and a coefficient of kinetic friction of 0.34. The correct solution involves using the force balance equation Ffriction + Fgravity = ma and solving for the acceleration, which is then used in the kinematic equation to find the time. The final solution is t = 0.82 seconds.
  • #1
Engineering101
6
0
Physics Help Greatly Appreciated -- Block sliding down ramp

A 7.7 kg block is on an incline with a coefficient of static friction of 0.50. The angle that the ramp makes with the horizontal is increased gradually, until the block begins to slide down the ramp. If you know that the coefficient of kinetic friction between the block and the plane is 0.34, find the time it will take the block to slide down the ramp a distance of 0.47 m starting from rest.


Ff=uFn




My solution:

arctan(.5)=angle of incline=26.6degrees
a=2x/t^2 (rearranged kinematic equation)
a=gsin(26.6)
a=4.39 m/s^2
4.39=2x/t^2
x=.47m
.94/4.39=t^2
t=.46 s

(This solution was marked incorrect) Help would be greatly appreciated.
 
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  • #2
It seems to me that you have calculated the time it would take if the coefficient of kinetic friction were zero.
 
  • #3
Vic is correct. Letting the acceleration = gsin(theta) gives the acceleration in the absence of friction. If you look at the force balance in the down incline direction it should read:

Ffriction + Fgravity = ma (1)

<< some extra work deleted by Mentor >>

Solve that to find the acceleration and the re-evaluate your kinematics equation.

Chris.
 
Last edited by a moderator:
  • #4
Alexander83 said:
Vic is correct. Letting the acceleration = gsin(theta) gives the acceleration in the absence of friction. If you look at the force balance in the down incline direction it should read:

Ffriction + Fgravity = ma (1)

<< some extra work deleted by Mentor >>

Solve that to find the acceleration and the re-evaluate your kinematics equation.

Chris.

Thanks for being willing and able to help with this question, Alexander. Just please remember that the OP student must do the bulk of the work. I think with the hints that he's been given now, he should be able to show us his work toward the correct solution.
 
  • #5
Thanks for the help! I genuinely appreciate it :)
I used
Fg-Ff=ma
mgsin(26.6)-umgcos26.6)=ma
9.8(sin26.6)-.32cos(26.6)=a
a=1.41
t=.82s
 

1. How does the angle of the ramp affect the speed of the block?

The angle of the ramp affects the speed of the block by changing the amount of gravitational force acting on the block. As the angle of the ramp increases, the component of the gravitational force acting parallel to the ramp also increases, causing the block to accelerate faster down the ramp.

2. What is the relationship between the mass of the block and its acceleration?

The relationship between the mass of the block and its acceleration is described by Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Therefore, a heavier block will experience less acceleration than a lighter block when acted upon by the same force.

3. How does friction affect the motion of the block down the ramp?

Friction between the block and the ramp will oppose the motion of the block, causing it to slow down. The amount of friction depends on the materials of the block and ramp, as well as the force pushing the block down the ramp. In some cases, the frictional force can be great enough to prevent the block from sliding down the ramp at all.

4. Is the potential energy of the block converted to kinetic energy as it slides down the ramp?

Yes, as the block slides down the ramp, its potential energy due to its position on the ramp is converted to kinetic energy. This is because the block is moving and has a velocity, which is a form of kinetic energy. The total energy of the block (potential energy + kinetic energy) remains constant throughout its motion.

5. How can the final velocity of the block be calculated using the ramp's angle and the block's initial velocity?

The final velocity of the block can be calculated using the conservation of energy principle, which states that the total energy of a system remains constant. By equating the initial potential energy of the block at the top of the ramp to its final kinetic energy at the bottom of the ramp, the final velocity can be determined using the formula: vf = √(vi² + 2gh), where vi is the initial velocity, g is the acceleration due to gravity, and h is the height of the ramp.

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