Answer:
GE = ME - 
, which agrees with option C in your list.
Explanation:
The definition of Mechanical Energy (ME) of a system is the addition of the gravitational potential energy (GE) plus the kinetic energy (KE) of the system:
ME = GE + KE
Given that the KE is: ,
solving for GE in the formula above gives:
GE = ME - KE = ME - , which agrees with option C
Answer:
1.8 m/s
Explanation:
Draw a free body diagram of the block. There are four forces:
Normal force Fn up.
Weight force mg down.
Applied force F to the east.
Friction force Fn μ to the west.
Sum the forces in the y direction:
∑F = ma
Fn − mg = 0
Fn = mg
Sum the forces in the x direction:
F − Fn μ = ma
F − mg μ = ma
a = (F − mg μ) / m
a = (12 N − 6 kg × 9.8 m/s² × 0.15) / 6 kg
a = 0.53 m/s²
Given:
Δx = 3 m
v₀ = 0 m/s
a = 0.53 m/s²
Find: v
v² = v₀² + 2aΔx
v² = (0 m/s)² + 2 (0.53 m/s²) (3 m)
v = 1.8 m/s
Answer:
Explanation:
Velocity is defined as the rate of change of displacement.
velocity is a vector quantity, that means it requires both magnitude and direction to completely explain the velocity.
For example, the velocity is 5 ms due east, it means an object is moving with speed 5 ms in the direction of east. We can say that the object covers the displacement of 5 m in one second due east.
(a) Let 
be the maximum linear speed with which the ball can move in a circle without breaking the cord. Its centripetal/radial acceleration has magnitude
where 
is the radius of the circle.
The tension in the cord is what makes the ball move in its plane. By Newton's second law, the maximum net force on it is
so that
Solve for :
(b) The net force equation in part (a) leads us to the relation
so that is directly proportional to the square root of . As the radius increases, the maximum linear speed will also increase, so the cord is less likely to break if we keep up the same speed.
