Max Height of Lamp Push for Sliding vs. Tipping

[IMGOOD]

Homework Statement

A person wants to push a lamp(mass 9.6 kg) across the floor a) Assuming the person pushes at a height of 60 cm above the ground and the coefficient of friction is 0.20, determine whether the lamp will slide or tip over b) Calculate the maximum height above the floor at which the person can push the lamp so that it slides rather than tips.
Hint: The base of the lamp is a flat metal disk of radius = 10 cm. If the lamp were to tip over, it would rotate around the bottom-right edge of this base.

Homework Equations

$$F_{net} = 0$$
$$\tau_{net} =0$$
$$\tau = Fd\sin(\theta)$$

The Attempt at a Solution

I don't know how would you figure out where the person can hold the lamp by using coefficient of friction in the equations.

 

[PhanthomJay]

Homework Statement

A person wants to push a lamp(mass 9.6 kg) across the floor a) Assuming the person pushes at a height of 60 cm above the ground and the coefficient of friction is 0.20, determine whether the lamp will slide or tip over b) Calculate the maximum height above the floor at which the person can push the lamp so that it slides rather than tips.
Hint: The base of the lamp is a flat metal disk of radius = 10 cm. If the lamp were to tip over, it would rotate around the bottom-right edge of this base.

Homework Equations

$$F_{net} = 0$$
$$\tau_{net} =0$$
$$\tau = Fd\sin(\theta)$$

The Attempt at a Solution

I don't know how would you figure out where the person can hold the lamp by using coefficient of friction in the equations.

How far from the right end of the base does the weight of the lamp act? Find the torque of ths weight force about the right end. Hint: Torque = Force times perpendicular distance from line of action of the force to the rotation point. Once you find that torque, what is the max force applied at 60cm that will make the 2 torques equal in magnitude but opposite in direction? Then work on the friction part. Show work, please.