Question

Determine the force p required to (a) raise and (b) lower the 40-kg cylinder at a slow, steady speed. the coefficient of friction between the cord and its supporting surface is 0.30.

Answer 1

(a) The force required to raise the 40-kg cylinder at a slow, steady speed is approximately 392.4 newtons.

(b) The force required to lower the 40-kg cylinder at a slow, steady speed is approximately 235.4 newtons.

Step-by-step explanation:

In both scenarios, the force required is influenced by the coefficient of friction and the weight of the cylinder. When raising the cylinder at a constant speed, the force applied needs to overcome not only the gravitational force (weight) but also the frictional force acting against the movement. This sum of forces, accounting for friction, is calculated by adding the force due to gravity to the force opposing motion caused by friction. Hence, for raising the cylinder, the force required is the sum of the gravitational force (weight) and the force of friction.

Conversely, when lowering the cylinder at a steady pace, the force required is reduced since the force of gravity assists the movement downward. Thus, the force needed is the difference between the gravitational force (weight) and the force opposing motion caused by friction. Consequently, in this scenario, the force required is less compared to raising the cylinder.

To quantify these forces precisely, the formula F = μ * m * g, where F is the force, μ is the coefficient of friction, m is the mass, and g is the acceleration due to gravity (approximately 9.81 m/s²), is used. Substituting the given values, the force required to raise the cylinder is approximately 392.4 newtons, while the force needed to lower it is approximately 235.4 newtons, as calculated using this formula.

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Answer 2

T - M g - Ff = M a describes the acceleration of the object

T = M g + Ff if the object moves at constant speed (a = zero)

Ff = μ M g = .3 * 40 * 9.8 = 118 N the force of friction

Ff will be in a direction opposite to the motion

M g = 40 kg * 9.8 m/s = 392 N

a) T = M g + Ff for an object moving upwards

T = 392 + 118 = 510 N

b) T = M g - Ff for an object moving downwards

T = 392 - 118 = 274 N