Variable mass of a toboggan down a slope

In summary, the problem involves a toboggan with a weight of 5.4kg and carrying 35kg of sand sliding down a 90m slope inclined at 30 degrees. The sand leaks from the back at a rate of 2.3kg/sec. The task is to find the time it takes for the toboggan to reach the bottom of the slope. The rocket equation mentioned in the previous equations does not apply here as the exhaust speed is zero. Instead, the equation Fdt=P-P' can be applied to solve the problem.
  • #1
karnten07
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1. Homework Statement

a 5.4kg toboggan carrying 35kg of sand slides from rest down an icy 90m slope inclined at 30 degrees below the horizontal. The sand leaks from the back of the toboggan at a rate of 2.3kgsec^-1. How long does it take the toboggan to reach the bottom of the slope?

2. Homework Equations
previous equations involved rockets and the equation:

v(final) = v(initial) + u ln(mi/mf)
where u is the exhaust speed

not sure if this relates to this question though?



3. The Attempt at a Solution

I drew the situation but can't see how to find the time, any suggestions please?
 
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  • #2
The rocket equation doesn't apply here. The exhaust speed is zero.
Apply Fdt=P-P' to your situation.
 

What is the concept of variable mass in relation to a toboggan going down a slope?

Variable mass refers to the idea that the mass of an object can change as it moves. In the case of a toboggan going down a slope, the mass can change due to factors such as the weight of the riders and the snow and ice that accumulate on the toboggan as it moves.

How does variable mass affect the speed of a toboggan going down a slope?

The variable mass of a toboggan can affect its speed in multiple ways. As the toboggan's mass increases, its inertia also increases, making it harder to accelerate. Additionally, a heavier toboggan will experience more friction and air resistance, further slowing it down. However, if the toboggan's mass decreases, it may be able to accelerate faster due to less inertia and friction.

What factors can cause the mass of a toboggan to change while going down a slope?

There are several factors that can cause the mass of a toboggan to change while going down a slope. These include the weight of the riders, the speed at which the toboggan is moving, and the amount of snow and ice that accumulates on the toboggan as it moves.

Does the variable mass of a toboggan affect its trajectory down a slope?

Yes, the variable mass of a toboggan can affect its trajectory down a slope. As the mass changes, the forces acting on the toboggan will also change, altering its acceleration and direction of motion. This can result in a different path down the slope compared to a toboggan with a constant mass.

How can the concept of variable mass be applied to other scenarios besides a toboggan going down a slope?

The concept of variable mass can be applied to many different scenarios, such as a rocket launching into space or a car accelerating on a road. In these cases, the mass of the object can change due to factors such as fuel consumption or passengers entering or exiting the vehicle. Understanding variable mass is important in accurately predicting the motion of objects in various situations.

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