<span>Let & be the angle between B und A. We have to show that B - |B|cos & A/|A| is normal to A. Using the dot product we must have (B - |B|cos & A/|A| )·A =0.
Since the dot product is distributive with respect to addition, we can write it as:
B·A - |B|cos & A/|A|·A = |B| |A|cos & - (|B|cos & A/|A|)|A|^2 = 0, since (|B|cos & A/|A|)|A|^2 = |B| |A|cos &.
hope this helps</span>
Answer:
57 N
Explanation:
Draw a free body diagram. There are three forces:
Weight force mg pulling down.
Normal force N pushing up.
Friction force F pushing horizontally.
Sum of the forces in the y direction:
∑F = ma
N − mg = 0
N = mg
Friction force is the product of normal force and coefficient of friction:
F = Nμ
F = mgμ
F = (65 kg) (9.8 m/s²) (0.09)
F = 57.3 N
Rounded, the friction force is 57 N.
The amount of energy before and after any energy transformations remain the same because energy cannot be created or destroyed. From the law conservation of energy; any time energy is transferred between two objects, or converted from one form into another, no energy is created and none is destroyed. The total amount of energy involved in the process remains the same.
Answer:
<h2>1) There is no work done by the machine because</h2><h2>B) The object has not moved</h2><h2>2) There is no work done by the prisoner because</h2><h2>D) The prisoner does no work because the wall goes no distance</h2><h2>3) The kinetic energy when it is half the way down is</h2><h2>6.0 J</h2>
Explanation:
1) As we know that the work done is the product of force and displacement
It is given as

so if the object is not displaced due to the force exerted by the object then the work done by the object must be ZERO
so correct answer is
B) The object has not moved
2) As we know that the work done is the product of force and displacement
It is given as

As we know that the wall is not displaced due to applied force so here work done by the prisoner must be zero
D) The prisoner does no work because the wall goes no distance
3) As we know by work energy theorem that work done by all forces is equal to change in its kinetic energy
So we will have

so we will have



now when cart moves half the distance then again using the same



Answer:
(a) -16.7 N s; (b) -167 N
Explanation:
Given: m = 0.530 kg; vi = 18.0 m/s; vf = 13.5 m/s; t = 0.100 s
Find: (a) Impulse, (b) Force
(a) Impulse = Momentum Change = m•Delta v = m•(vf - vi)= (0.530 kg)•( -13.5 m/s - 18.0 m/s)
Impulse = -16.7 kg•m/s = -16.7 N•s
where the "-" indicates that the impulse was opposite the original direction of motion.
(Note that a kg•m/s is equivalent to a N•s)
(b) The impulse is the product of force and time. So if impulse is known and time is known, force can be easily determined.
Impulse = F•t
F = Impulse/t = (-16.7 N s) / (0.100 s) = -167 N
where the "-" indicates that the impulse was opposite the original direction of motion.