Help with Two Problems: Table Overturn & Cube Sliding/Tipping

[ninjagowoowoo]

I have here two problems that I can't even touch. Please someone help me!

A 36.6 kg round table is supported by three legs placed equal distances apart on the edge. What minimum mass, placed on the table's edge, will cause the table to overturn? Neglect the mass of the legs.

A cube of side l = 120 cm rests on a rough floor. It is subjected to a steady horizontal pull, F, exerted a distance h = 83.0 cm above the floor. As F is increased, the block will either begin to slide, or begin to tip over. What is the maximum coefficient of static friction for which the block begins to slide rather than tip? Wouldn't I ned to know F to figure this out?

 

[Nate810]

For the first problem, you need to calculate the torque. The minimum mass that will cause the table to overturn is equal to the torque created by the equal weight of the legs. The formula for torque is T = F * r, where F is the force applied and r is the radius of the table. For the second problem, you need to calculate the maximum static friction force. You can calculate this using the equation F_max = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force exerted on the cube. The normal force is equal to the weight of the cube, so N = mg, where m is the mass of the cube and g is the gravitational acceleration.

 

[thepatientmental]

For the first problem, the minimum mass needed to cause the table to overturn can be calculated using the principle of moments. Since the table is supported by three legs, it forms a triangle. The weight of the table acts downwards at its center of mass, while the force causing it to overturn acts at the edge of the table. To prevent the table from overturning, the moment created by the weight of the table must be equal to or greater than the moment created by the force at the edge.

Using the equation M = F x d, where M is the moment, F is the force, and d is the distance from the point of rotation, we can set up the following equation:

M(weight of table) = M(force at edge)

mg x l/2 = F x l/3

where m is the mass of the table, g is the acceleration due to gravity, and l is the distance between the legs.

Solving for F, we get F = 3mg/2. This means that the minimum force required to overturn the table is 1.5 times the weight of the table. Therefore, the minimum mass required to cause the table to overturn is 1.5 times the mass of the table, which is 54.9 kg.

For the second problem, we can use the concept of torque to determine the maximum coefficient of static friction. Torque is the product of force and distance, and it is a measure of the tendency of a force to rotate an object around an axis.

In this case, the force F is causing the cube to either slide or tip over. The torque created by this force can be calculated as T = F x h, where T is the torque, F is the force, and h is the distance from the point of rotation (in this case, the edge of the cube).

The maximum coefficient of static friction can be found when the torque created by the force F is equal to the torque created by the weight of the cube. This means that the cube is on the verge of tipping over. Therefore, we can set up the following equation:

T(force causing sliding) = T(force causing tipping)

F x h = mg x l/2

where m is the mass of the cube, g is the acceleration due to gravity, and l is the length of one side of the cube.

Solving for the coefficient of friction, we get μ = (mg x l/2