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.

 

[m2003]

I would approach this problem by first understanding the physics principles involved. In this case, we are dealing with forces and torques. The person's push on the lamp creates a force, and if this force is greater than the force of friction between the lamp and the floor, the lamp will slide. If the force is less than the force of friction, the lamp will tip over.

To determine whether the lamp will slide or tip over, we need to calculate the force of friction and the torque created by the person's push. The force of friction can be calculated using the formula F_friction = μN, where μ is the coefficient of friction and N is the normal force (in this case, the weight of the lamp). The normal force can be calculated using the formula N = mg, where m is the mass of the lamp and g is the acceleration due to gravity.

To calculate the torque created by the person's push, we need to know the distance between the point where the force is applied (in this case, the person's hand) and the point where the lamp would rotate around if it were to tip over (in this case, the bottom-right edge of the base). This distance can be calculated by taking the height of the person's hand (60 cm) and adding it to the radius of the base (10 cm). The torque can then be calculated using the formula τ = Fd sin(θ), where F is the force applied, d is the distance, and θ is the angle between the force and the lever arm (in this case, 90 degrees).

If the torque created by the person's push is greater than the torque created by the force of friction, the lamp will tip over. To prevent this from happening, the maximum height at which the person can push the lamp without it tipping over can be calculated by setting the two torques equal to each other and solving for the height. This can be done using the equation τ = F_frictiond, where d is the distance calculated earlier.

In conclusion, to determine whether the lamp will slide or tip over, we need to compare the force of friction and the torque created by the person's push. To calculate the maximum height at which the person can push the lamp without it tipping over, we need to set the two torques equal to each other and solve for the height.