Answer:
u" + 40u' + 49u = 2 sin(t/6)
upp + 40up + 49u = 2 sin(t/6)
Explanation:
Step 1: Data given
mass = 5 kg
L = 20 cm = 0.2 m
F = 10 sin(t/6)N
Fd(t) = - 6 N
u(0) = 0.03 m/s
u(0) = 0
u'(0) = 3 cm/s
Step 2:
ω =kL
k = ω/L = m*g /L = (5*9.8)/0.2 = 245 kg/s²
Since Fd(t) = -γu'(t) we know:
γ =- Fd(t) / u'(t) = 6N/ 0.03 m/s = 200 Ns/m
The initial value problem which describes the motion of the mass is given by
5u" + 200u' + 245u = 10 sin(t/6) u(0) = 0 ; u'(0) = 0.03
This is equivalent to:
u" + 40u' + 49u = 2 sin(t/6) u(0) = 0 ; u'(0) = 0.03
upp + 40up + 49u = 2 sin(t/6)
With u in m and t in s
Answer:
In a circular motion, the object just moves in a circle. In rotational motion, the object rotates about an axis. ... For example, Earth rotating on its own axis.
Answer:
A permanent magnet creates a magnetic field at all points in the surrounding region.
An electric current in a conductor creates a magnetic field at all points in the surrounding region.
A moving electric charge creates a magnetic field at all points in the surrounding region.
Explanation:
Magnet field is a region around the magnet in which the magnetic force can be experienced. A magnet has two poles: North pole and South pole. A Magnetic field originates from north pole and ends at south pole.
Magnets are of two types: Permanent magnet and temporary magnet.
A moving charge produces magnetic field. A stationary charge can not produce a magnetic field.
The rate of flowing charge constitutes an electric current. If the cardboard is placed around the current carrying conductor and the iron fillings spread around the cardboard then the iron nails get stick to it. It means that a current carrying conductor creates a magnetic field around it.
Therefore, the true statements from the given statements are as follows;
A permanent magnet creates a magnetic field at all points in the surrounding region.
An electric current in a conductor creates a magnetic field at all points in the surrounding region.
A moving electric charge creates a magnetic field at all points in the surrounding region.
Answer:
The resultant force would (still) be zero.
Explanation:
Before the 600-N force is removed, the crate is not moving (relative to the surface.) Its velocity would be zero. Since its velocity isn't changing, its acceleration would also be zero.
In effect, the 600-N force to the left and 200-N force to the right combines and acts like a 400-N force to the left.
By Newton's Second Law, the resultant force on the crate would be zero. As a result, friction (the only other horizontal force on the crate) should balance that 400-N force. In this case, the friction should act in the opposite direction with a size of 400 N.
When the 600-N force is removed, there would only be two horizontal forces on the crate: the 200-N force to the right, and friction. The maximum friction possible must be at least 200 N such that the resultant force would still be zero. In this case, the static friction coefficient isn't known. As a result, it won't be possible to find the exact value of the maximum friction on the crate.
However, recall that before the 600-N force is removed, the friction on the crate is 400 N. The normal force on the crate (which is in the vertical direction) did not change. As a result, one can hence be assured that the maximum friction would be at least 400 N. That's sufficient for balancing the 200-N force to the right. Hence, the resultant force on the crate would still be zero, and the crate won't move.
A. attract each other.
The Law of Universal Gravitation discusses the phenomenon of gravity. Remember that gravity is the force that keeps us on Earth; the Earth pulls us down, and our bodies pull back. Gravity is the force of attraction, so the correct answer is a).
