(a) Find the work done by the cord's force on the block.
WF = -T * d
(b) Find the work done by the weight of the block.
Wg = mg * d
(c) Find the kinetic energy of the block.
K = 1/2 * mv^2
(d) Find the speed of the block.
v = sqrt(2gd) .
(a) Work done by the cord's force on the block
The cord's force is acting upwards, opposing the force of gravity. Therefore, the work done by the cord's force is negative.
WF = -T * d
where T is the tension in the cord and d is the distance the block has fallen.
To find the tension in the cord, we can use the equation of motion:
m * a = T - mg
where m is the mass of the block, a is the acceleration of the block, and g is the acceleration due to gravity.
Plugging in the values given in the problem, we get:
M * (g/4) = T - Mg
Solving for T, we get:
T = 3Mg/4
Therefore, the work done by the cord's force on the block is:
WF = -3Mgd/4
(b) Work done by the weight of the block
The weight of the block is acting downwards, in the same direction as the block's motion. Therefore, the work done by the weight of the block is positive.
Wg = mg * d
where mg is the weight of the block and d is the distance the block has fallen.
Plugging in the values given in the problem, we get:
Wg = Mgd
(c) Kinetic energy of the block
The kinetic energy of the block is given by:
K = 1/2 * mv^2
where m is the mass of the block and v is the speed of the block.
We can find the speed of the block using the conservation of energy principle:
Work done = Change in kinetic energy
WF + Wg = K
Plugging in the values we found, we get:
-3Mgd/4 + Mgd = 1/2 * Mv^2
Solving for v, we get:
v = sqrt(2gd)
Therefore, the kinetic energy of the block is:
K = 1/2 * M * (sqrt(2gd))^2 = Mgd
(d) Speed of the block
v = sqrt(2gd)
Question
A cord is used to vertically lower an initially stationary block of mass M kg at a constant downward acceleration of g/4. The block has fallen a distance d. (Use any variable or symbol stated above as necessary.)
(a) Find the work done by the cord's force on the block.
WF = __________
(b) Find the work done by the weight of the block.
Wg = ___________
(c) Find the kinetic energy of the block.
K = _________
(d) Find the speed of the block.
v = __________