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By Newton's third law, if the rope is pulling on the boat with some force, then the boat is pulling on the rope with this same force. So either terminology is fine. By attaching the rope to the boat and by there being tension in the rope, the rope and boat are now pulling on each other.
Your proposition that $T\leq T_0e^{-\mu\theta}$ doesn't make sense, as ...
2
Why can't I take the surface as a part of system and conserve momentum?
Technically, you can. Experimentally, this will be difficult.
As the surface is basically earth, as it's mass is so huge it's velocity change is negligible and I can cancel it's momentum on πΏπ»π and π
π»π when I write ππ=ππ.
Its velocity change is indeed negligible (and in ...
2
Problems like these can best be approached with a Free Body Diagram (the vertical is the $y$-axis and the horizontal the $x$-axis):
We can see that (with no movement in the vertical direction):
$$F_N=mg$$
Since as the spring is compressed, the friction force $F_f$ points to the wall (assume the static case - index $s$):
$$F_f=\mu_sF_N=\mu_s mg$$
Now we can ...
2
Mathematical analysis
The net momentum imparted by the friction force on your body is zero. Mathematically,
$$\Delta \mathbf p =\int_0^T \mathbf F(t)\: \mathrm dt =0\tag{1}$$
where $\mathbf F(t)$ is the friction force acting on you at any time $t$. Now, since you have the same velocity at every instant, thus the integral in equation $(1)$ should evaluate to $...
1
The key is that the force propelling the (super)man forwards is a Newtonian reaction force from the (super)man pushing backwards on the ground. By Newton's third law, the force pushing forwards on the runner is equal to the force pushing backwards.
A normal human is unable to exert so much force on the ground that their good-quality trainers slip (try it), ...
1
We aren't interested in the bulk motion of the vehicle, only the relative motion of the part of the car touching the road (the bottom of the wheel).
It's often useful to imagine what would happen if we turned friction to zero. We'll let the car move forward a bit and then turn it off.
As the accelerator pedal is pressed, the wheel will slip and spin forward....
1
Frictional force, and any other force for that matter, is the same in an inertial and a non-inertial frame of reference. In the non-inertial frame, only an extra force $-MA$, called the pseudoforce or fictitious force is necessary to get the correct equations of motion.
1
Will friction act in the south direction and the west direction
respectively, or will friction act only in the south west direction
combined and the block move in the north east direction with some
acceleration ?
As @Warrenmovic pointed out, the friction force will be in the opposite direction of the resultant force, i.e., $\sqrt 2$ N in the south west ...
1
This is how I deal with problem of finite friction.
Assume friction is infinite and find the required friction force needed to resist all relative motion. Lets say this results into two co-planar friction forces $F_x$ and $F_y$.
Calculate the magnitude of the required friction force $F = \sqrt{F_x^2+F_y^2}$
Compare the magnitude $F$ to the actual available ...
1
Friction always acts opposing the motion of the object. So if you have a resultant force in a particular direction, friction will always act in the opposite direction. So if your particle is moving north-west due to a force, friction will act to oppose that motion (hence south-east), hope that helps.
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loose sand has no shear strength. This is why bike wheels skid on sand: the sand adheres to the tire, but that sand shears loose from the rest of the sand. Then you fall down go BOOM.
1
Well, there's gravity, but I'm assuming you aren't referring to that. I'm assuming you're referring to pushing against the ground horizontally.
When your foot is on the ground, static friction holds the foot in place. However, the rest of the body can move, starting from the ankles and moving upwards. We basically end up pushing the body away from the ...
1
Given a force field $\vec{F}(\vec{x})$, the curl being zero everywhere is a necessary and sufficient condition for $\vec{F}$ to be conservative. But the frictional force $\vec{F}=-b\vec{v}$ is not a field at all, so this does not apply.
Writing $\vec{\nabla}\times\vec{F}$ does not even make sense for this force, since curl is only defined for vector fields, ...
1
But there is a net friction force on me which is making me walk. Now
according to me there are no other forces acting. Shouldn't that mean
that I should be accelerating but I am not accelerating?
As @FakeMod pointed out its answer, you are alternatively accelerating and decelerating in such a way that your overall average velocity is constant.
Consider when ...
1
What happens is that the water forms a seal between the steel glass and the glass table.
Due to the slightly higher pressure $p$ inside the glass it's kept afloat while the inside pressure is maintained because of the seal. The slight over-pressure arises when the glass 'sinks' into the water layer and is caused by the weight of the glass, which slightly ...
1
because as we know when relative velocity is zero , friction shouldn't act.
This is false. Static friction acts when the relative velocity between surfaces is $0$. For a simple example, take a heavy object and start pushing on it without it moving. Static friction is the force that opposes your applied force before the object starts moving.
Because of this, ...
1
While Gert's answer implies this, your main issue is in assuming that static friction is equal to $\mu N$ here. For static friction, $\mu N$ is the maximum value static friction can take, but generally static friction will be less than this value.
Therefore, all we can say for the net force acting on the object along the incline is $$ma=mg\sin\theta-F_s$$
...
1
So that leads me to ask why is $\mu$ different for a solid sphere and
a shell, as it appears it must be?
The $\mu$ don't have to be different or the same. Depending on the inclination $\theta$ only a part of the potentially available friction force is used to prevent sliding. Assuming roughness is sufficient, neither rolling objects will start slipping, ...
1
Friction
Friction appears when there is some impending or happening relative motion between the surfaces of two bodies. When there's no relative motion between two surface, there can still be friction to prevent any impending relative motion. This friction is known as static friction. When two bodies' surfaces are moving relative to each other, the friction ...
1
Kinetic friction acts at every point of the block, and so does the normal force. The offset location of the normal force is just a way of sidestepping the summing the torque of normal forces acting at every point. This is similar to defining the center of mass, which is the point where all the mass can be assumed to be concentrated (not always, though). In a ...
1
There is a method I've developed for solving a tricky friction problem like this that always works, and never fails to deliver the desired understanding. I'm going to present it here for the laboratory frame of reference (the more complicated case) and leave it to you to apply to the belt frame of reference situation.
The method involves treating the ...
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