Answer:
Explanation:
Torque is defined as the cross product between the position vector ( the lever arm vector connecting the origin to the point of force application) and the force vector.
Due to the definition of cross product, the magnitude of the torque is given by:
Where is the angle between the force and lever arm vectors. So, the length of the lever arm (r) is minimun when
is equal to one, solving for r:
Answer:
The maximum height reached by the two blocks is approximately 0.1147959 × v₀²
Explanation:
The mass of block B = m
The mass of block A = 3·m
The initial velocity of block B, v₂ = 0 m/s
The initial velocity of block A, v₁ = v₀
The amount of friction between the blocks and the surface = Negligible friction
By the Law of conservation of linear momentum, we have;
Total initial momentum = Total final momentum
3·m·v₁ + m·v₂ = (3·m + m)·v₃ = 4·m·v₃
Plugging in the values for the velocities gives;
3·m × v₀ + m × 0 = (3·m + m)·v₃ = 4·m·v₃
∴ 3·m × v₀ = 4·m·v₃
The kinetic energy, K.E. of the combined blocks after the collision is given as follows;
K.E. = 1/2 × mass × v²
The potential energy, P.E., gained by the two blocks at maximum height = The kinetic energy, K.E., of the two blocks before moving vertically upwards
The potential energy, P.E. = m·g·h
Where;
m = The mass of the object at the given height
g = The acceleration due to gravity
h = The height at which the object of mass, 'm', is located
Therefore, for h = The maximum height reached by the two blocks, we have;
P.E. = K.E.
The maximum height reached by the two blocks, h ≈ 0.1147959·v₀².