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.

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

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