What is the magnitude of the force you must exert on the rope in order to accelerate upward at 1.4 m/s2, assuming your inertia is 63 kg? Express your answer with the appropriate units.

The magnitude of the force you must exert on the rope in order to accelerate upward is 705.6 N

Explanation:

The magnitude of force, you must exert can be estimated as follows;

Since it is upward motion, we must consider acceleration due to gravity which opposes the upward motion.

F = m (a+g)

where;

F is the magnitude of the upward force

m is your mass, which is the measure of inertia = 63kg

a is the acceleration of the rope = 1.4 m/s²

F = 63 (1.4 + 9.8)

F = 63 (11.2)

F = 705.6 N

Therefore, the magnitude of the force you must exert on the rope in order to accelerate upward is 705.6 N

705.6 N

Explanation:

Force: This can be defined as the product of mass a acceleration.

The S. I unit of force is Newton.

The expression for the force on the rope in order to accelerate upward is given as,

F-W = ma ... Equation 1

Where F = Force exerted on the rope, W = weight of the rope, m = mass of the rope, a = acceleration.

But,

W = mg ... Equation 2

Where g = acceleration due to gravity

substitute equation 2 into equation 1

F-mg = ma

F = ma+mg

F = m (a+g) ... Equation 3

Given: m = 63 kg, a = 1.4 m/s²

Constant: g = 9.8 m/s²

Substitute into equation 3

F = 63 (1.4+9.8)

F = 63 (11.2)

F = 705.6 N

The magnitude of the force exerted on the rope = 705.6 N