Force to push mass down inclined plane

AI Thread Summary
To keep a 40 kg mass sliding down a frictionless ramp at a 30-degree angle at constant velocity, the force applied must counteract the component of the mass's weight along the incline. This force is calculated using the formula mgcos(30), where m is the mass and g is the acceleration due to gravity. The net force on the mass is zero when it moves at constant velocity, meaning the applied force equals the gravitational component down the ramp. Understanding the normal force is also essential for further calculations, although friction is not a factor in this scenario. The discussion highlights the importance of reviewing forces acting on objects on inclined planes.
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Homework Statement



The angle of the ramp is 30 degrees. The mass is 40 kg. What force must be applied to keep the mass sliding down the ramp at constant velocity. The ramp is frictionless*

Homework Equations


I have missed the past few lessons in class, so I'm not sure. I do have a bunch of equations, but I have little clue on how to use them for this problem

The Attempt at a Solution

 
Last edited:
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Assuming there is no friction, the force required to cause the mass to move at a constant rate is equal to the component of the mass's weight down the 30-degree incline. When this happens, the total net force on the mass is zero as the accelerative force (gravity) is canceled out, and it moves at a constant rate. The component of weight down the ramp is given by the expression mgcos(30). This, the force required is mgcos(30), or (40 kg)(9.8 m/s/s)(.866). It will be directed in the direction opposite the component of gravity down the ramp.
 
You might begin with a review of the forces on a block on a ramp.
You will need to find the normal force pushing the block against the ramp in order to calculate the friction force. Nice diagram here:
http://en.wikiversity.org/wiki/Motion_in_two_dimensions
 
I got it, thanks guys
 
Last edited:
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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