Forces on a slab of mass Question

In summary, a slab of mass 40 kg rests on a frictionless floor and a block of mass 10 kg rests on top of the slab. The coefficient of static friction between the two is 0.60 and the coefficient of kinetic friction is 0.40. When a horizontal force of 100 N is applied to the block, the maximum static friction force between the two is 60 N. As the applied force exceeds 60 N, the block will start to slip and kinetic friction will act on both the block and the slab, causing them to have different accelerations. The resulting accelerations can be calculated using the values of the respective forces.
  • #1
bjgawp
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Homework Statement


A slab of mass [tex]m_{1} = 40 \mbox{kg}[/tex] rests on a frictionless floor and a block [tex]m_{2} = 10 \mbox{kg}[/tex] rests on top of the mass. Between the block and the slab, the coefficient of static friction is 0.60 and the coefficient of kinetic friction is 0.40. The block ontop of the mass is pulled by a horizontal force of 100 N. What are the resulting accelerations of the block and the slab?


Homework Equations





The Attempt at a Solution


What I'm having trouble is identify the forces. My friend says that with the force being applied on [tex]m_{2}[/tex], there would be friction resisting the motion. Consequently, a force of the same magnitude of the mentioned friction force would occur on [tex]m_{1}in the direction of the applied force[/tex]. How does that work?
 
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  • #2
The max value of static friction possible between the two is [tex]\mu_sm_2g[/tex] =0.60*10*10=60 N.
Since the applied force is 100 N, definitely there will be slipping between the block and the slab and ultimately, they will get separated.

Until they get seperated, Kinetic friction will act and both of them will have different accelerations.

[tex]f_k=\mu_km_2g[/tex]=40 N acting on [tex]m_2[/tex] in the backward direction and on [tex]m_1[/tex] in forward direction.

so [tex]a_1= [/tex]<< solution deleted by berkeman >>



and [tex] a_2=[/tex]<< solution deleted by berkeman >>
_________
I may be wrong.
 
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  • #3


As a scientist, it is important to first accurately identify and label all the forces acting on the system. In this scenario, there are several forces at play: the force of gravity acting on both masses, the normal force from the floor on the slab, the normal force from the slab on the block, and the frictional forces between the block and the slab.

In order to determine the accelerations of the block and the slab, we can use Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration. In this case, the net force on the block will be the applied force of 100 N minus the frictional force between the block and the slab, which is equal to 0.6 times the normal force between the two masses.

Therefore, the net force on the block can be written as F_{net} = 100 N - 0.6(m_{2}g) = m_{2}a_{2}, where g is the acceleration due to gravity and a_{2} is the acceleration of the block.

Similarly, the net force on the slab can be written as F_{net} = 0.4(m_{2}g) = m_{1}a_{1}, where a_{1} is the acceleration of the slab.

Solving for the accelerations, we get a_{2} = 4.9 m/s^2 and a_{1} = 1.2 m/s^2.

As for your question about the frictional force on the slab, your friend is correct in saying that there will be a reactionary force on the slab in the direction of the applied force on the block. This is due to Newton's third law, which states that every action has an equal and opposite reaction. In this case, the applied force on the block will also result in a frictional force on the slab in the opposite direction. This force will be equal in magnitude to the frictional force between the block and the slab, but it will act on the slab instead of the block.
 

Related to Forces on a slab of mass Question

1. What is the definition of "forces on a slab of mass"?

"Forces on a slab of mass" refers to the external forces acting on a slab or flat surface with a certain amount of mass. These forces can include gravity, friction, and any other force that may be acting upon the slab.

2. How do you calculate the net force on a slab of mass?

The net force on a slab of mass can be calculated by adding up all the external forces acting on the slab. This can be done by using Newton's second law of motion, which states that the net force is equal to the mass of the object multiplied by its acceleration.

3. What factors affect the forces acting on a slab of mass?

The forces acting on a slab of mass are affected by several factors, including the mass of the slab, the angle at which the force is applied, and the type of surface the slab is resting on. Other external factors, such as air resistance, can also affect the forces acting on the slab.

4. How do you determine the direction of the net force on a slab of mass?

The direction of the net force on a slab of mass is determined by the direction of the external forces acting on the slab. If the forces are acting in the same direction, the net force will also be in that direction. If the forces are acting in different directions, the net force will be in the direction of the stronger force.

5. What happens to the forces on a slab of mass when it is in motion?

When a slab of mass is in motion, the forces acting on it can change. For example, if the slab is sliding on a surface, the force of friction will increase as the speed increases. Additionally, if the slab is dropped, the force of gravity will increase as it falls. These changes in forces can affect the acceleration and overall motion of the slab.

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