Motion of a block on a steep surface

In summary, the problem involves finding the ratio of time taken for a block to travel up and down a slope with initial velocity and frictional force. The trick to solving the motion up the slope involves using the same time for moving a certain distance from rest, regardless of initial velocity. This can be calculated by considering the area under a velocity/time graph.
  • #1
diredragon
323
15

Homework Statement


The block was given an initial velocity up the surface with an angle of 45 degrees to the ground. Calculate the ##\frac{t_1}{t_2}## with ##t_1## being the time it took to get to the highest point up the hill and ##t_2## the time it took to get down. In both cases the frictional force with coefficient m= 0.2 was acting on it.
2. Homework Equations
3. The Attempt at a Solution
My tried solution is uploaded below in form of a picture.
I have made free body diagrams but am stuck at getting the equation that involves time so that i can divide the two times. Any hints?
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  • #2
diredragon said:
I have made free body diagrams but am stuck at getting the equation that involves time so that i can divide the two times. Any hints?

Think generally: if a body moves a distance ##d## how does the time depend on the acceleration?
 
  • #3
PeroK said:
Think generally: if a body moves a distance ##d## how does the time depend on the acceleration?

##d=v_ot + \frac{1}{2}at^2##
Im still kinda stuck...
 
  • #4
diredragon said:
##d=v_ot + \frac{1}{2}at^2##
Im still kinda stuck...

The body goes the same distance up the slope as it does down the slope. Down the slope is easy, as ##v_o = 0##.

You can use a trick for motion up the slope: the time taken to move a distance ##d## from an initial velocity to rest at deceleration ##a## is the same as the time to move a distance ##d## from rest at acceleration ##a##. This avoids needing to calculating ##v_0##.

To see this, think about distance as the area under a velocity/time graph.
 
  • #5
PeroK said:
The body goes the same distance up the slope as it does down the slope. Down the slope is easy, as ##v_o = 0##.

You can use a trick for motion up the slope: the time taken to move a distance ##d## from an initial velocity to rest at deceleration ##a## is the same as the time to move a distance ##d## from rest at acceleration ##a##. This avoids needing to calculating ##v_0##.

To see this, think about distance as the area under a velocity/time graph.

I don't understand the trick, so in the new equation for the motion up the slope i would not have ##v_o## but would have some new ##a## while d stays the same right? How would i make that work?
 
Last edited:

1. What factors affect the motion of a block on a steep surface?

The motion of a block on a steep surface is affected by several factors, including the angle of the surface, the mass of the block, and the coefficient of friction between the block and the surface. Other factors such as air resistance and external forces may also play a role.

2. How does the angle of the surface impact the motion of the block?

The steeper the surface, the greater the force of gravity acting on the block. This means that the block will accelerate faster down a steep surface compared to a more gradual one. Additionally, a steeper surface will have a higher coefficient of friction, which can also affect the motion of the block.

3. How does the mass of the block affect its motion on a steep surface?

The mass of the block affects its motion on a steep surface by increasing the force of gravity acting on the block. This means that a heavier block will accelerate faster down a steep surface compared to a lighter block. However, the mass of the block also affects its inertia, which can impact its ability to resist changes in motion.

4. What is the role of friction in the motion of a block on a steep surface?

Friction is the force that opposes the motion of an object. On a steep surface, friction plays a crucial role in slowing down the motion of the block. The higher the coefficient of friction between the block and the surface, the greater the force of friction acting on the block, which can significantly impact its motion.

5. How do external forces impact the motion of a block on a steep surface?

External forces, such as a push or pull, can affect the motion of a block on a steep surface. If the external force is greater than the force of friction and the force of gravity, it can cause the block to accelerate or decelerate in a different direction. External forces can also cause the block to change direction or come to a stop if they are strong enough.

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