Help with Newton's second and third laws

[hollymason]

Homework Statement

Two blocks are pushed to the right so that they move together with increasing speed. Block B remains at the height shown. Ignore friction between the ground and block A but not between block A and block B. The mass of block A is 10kg and the mass of block B is 2kg. Let system S represent the system consisting of both blocks A and B. (use g=10m/s^2)A-for block a, b, and system s: draw free-body diagrams, identify any Newton's third law force pairs, and write out the algebraic form of Newton's second law.

B-using only the forces in your free-body diagram for system S, calculate the magnitude of the force exerted on system C by the ground (N_sg).

C-using only the forces in your free-body diagrams for block A and block B, calculate the magnitude of the force exerted on block A by the ground (N_ag).

D- How should the value of N_sg compare to N_ag?

Homework Equations

Force = mass X acceleration

The Attempt at a Solution

[/B]
This is my attempt so far. I'm stuck on C because I feel like I would use the same equation F=m X a but mass would be 10kg instead of 12 because it's asking about the force exerted on A. But the blocks move together so would I account for the weight of B as well? I've attached an image so you can see my attempt at parts A and B as well.

http://oi58.tinypic.com/2z4gw11.jpg

 

[Doc Al]

I'm stuck on C because I feel like I would use the same equation F=m X a but mass would be 10kg instead of 12 because it's asking about the force exerted on A.

OK.

But the blocks move together so would I account for the weight of B as well?

The weight of B only acts directly on B, not A. Of course, the weight of B affects the force that B exerts on A. Set up two equations, one for A and one for B.

 

[hollymason]

Sorry if this is a stupid question, but do you mean write different force equations for A and B?
So for A it would be F=10kg X 10m/s2=100N
and for B it would be F=2kg X 10m/s2 = 20N

 

[Doc Al]

Sorry if this is a stupid question, but do you mean write different force equations for A and B?
So for A it would be F=10kg X 10m/s2=100N
and for B it would be F=2kg X 10m/s2 = 20N

I mean apply Newton's 2nd law to each block separately. ($\Sigma F = ma$.) You already have the forces identified, and even the equations written. (To answer part C, all you need are the vertical forces.)

 

[HalfLostAndSearching]

A) The free-body diagram for block A shows the force of gravity (W_A = m_Ag), the normal force from block B (N_AB), and the applied force (F_A). The free-body diagram for block B shows the normal force from block A (N_BA), the normal force from the ground (N_BG), and the force of gravity (W_B = m_Bg). The free-body diagram for system S shows the applied force (F_A), the normal force from block A (N_AB), and the normal force from the ground (N_SG).

B) Using the equation F=ma, we can calculate the net force on system S by adding the forces in the x-direction. F_net = F_A - N_AB - N_SG = ma. Since the blocks are moving together with increasing speed, we can assume that the net force is positive and is equal to the mass of the system (m_A + m_B) multiplied by the acceleration (a). Therefore, F_A - N_AB - N_SG = (m_A + m_B)a.

C) To calculate the force exerted on block A by the ground (N_AG), we can use the same equation F=ma. However, since we are only considering the forces on block A, the mass in this equation would be m_A. The net force on block A is equal to the applied force (F_A) minus the normal force from block B (N_AB) and the force of gravity (W_A = m_Ag). Therefore, F_A - N_AB - W_A = m_Aa. We can solve for N_AG by adding N_AB and W_A to both sides of the equation, giving us N_AG = F_A - m_Aa.

D) The value of N_SG should be greater than N_AG. This is because N_SG takes into account the normal force from block B, which is also exerting a force on block A. Therefore, the normal force from the ground must be greater in order to keep the blocks moving together with increasing speed.