Two horizontal forces,

P and Q, are acting on a block that is placed on a table. We know that
P =(−1.10i + 4.25k) N
but the magnitude and direction of
Q are unknown. The block moves along the table. Assume there is no friction between the object and the table. Here the mass of the block is 4.10 kg.

a) What is Q when velocity is constant?

b)Determine the force
Q when the acceleration of the block is (−4.50i + 2.25k) m/s^2.
Express your answer in vector form.

c) Determine the force
Q when the acceleration of the block is (4.50i − 2.25k) m/s^2. Express your answer in vector form.

So far I know that a) is just
Q =(1.10i - 4.25k) N

when velocity is constant, Q=-P

b)
Net force=ma
P+Q=ma
Q= ma-P
= 4.1((3.5i-2.25k)-( −1.10i + 4.25k)
you can do that.

c? same as b.

for b) and c), determine the force (Q) using the acceleration components and the components of (P) ... you have the mass of the block

f = m a ... by components

a) Ah, the mystery of Q's magnitude and direction. Well, when the velocity is constant, it means there is no acceleration. Since there is no friction to oppose the motion, we can assume that the two forces P and Q are balanced, leading to a net force of zero. So, Q must be equal to -P to keep things in equilibrium.

b) Now, when the acceleration of the block is (-4.50i + 2.25k) m/s^2, we need to find the net force acting on the block. Since F = ma, where F is the net force, m is the mass, and a is the acceleration, we can plug in the values and solve for Q.

F = ma
Q + P = ma
Q = ma - P

Substituting the given values,
Q = (4.10 kg)(-4.50i + 2.25k) m/s^2 - (-1.10i + 4.25k) N

Now, do some calculations to find the force Q, and express your answer in vector form.

c) Similarly, when the acceleration is (4.50i - 2.25k) m/s^2, we can use the same formula to find Q.

Q = ma - P

Plug in the given values and perform the necessary calculations to determine the force Q, expressing your answer in vector form.

To solve these problems, we need to apply Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration:

F = m * a

In this case, the mass of the block is given as 4.10 kg.

a) To find the force Q when the velocity is constant, we can use the fact that the net force acting on the block is zero because the velocity is constant. So:

P + Q = 0

Since P is given as (-1.10i + 4.25k) N, we can solve for Q:

Q = -P
= -(-1.10i + 4.25k) N
= (1.10i - 4.25k) N

Therefore, the force Q when the velocity is constant is (1.10i - 4.25k) N.

b) To determine the force Q when the acceleration of the block is (-4.50i + 2.25k) m/s^2, we can again apply Newton's second law. Substituting the given values:

P + Q = m * a

(-1.10i + 4.25k) + Q = (4.10 kg) * (-4.50i + 2.25k)

Now, we can solve for Q by isolating it on one side of the equation:

Q = (4.10 kg) * (-4.50i + 2.25k) - (-1.10i + 4.25k) N
= (-18.45i + 9.22k + 1.10i - 4.25k) N
= (-17.35i + 4.97k) N

Therefore, the force Q when the acceleration of the block is (-4.50i + 2.25k) m/s^2 is (-17.35i + 4.97k) N.

c) Similarly, to find the force Q when the acceleration of the block is (4.50i - 2.25k) m/s^2, we use the same equation:

P + Q = m * a

(-1.10i + 4.25k) + Q = (4.10 kg) * (4.50i - 2.25k)

Again, we isolate Q and solve for it:

Q = (4.10 kg) * (4.50i - 2.25k) - (-1.10i + 4.25k) N
= (18.45i - 9.22k + 1.10i - 4.25k) N
= (19.55i - 13.47k) N

Therefore, the force Q when the acceleration of the block is (4.50i - 2.25k) m/s^2 is (19.55i - 13.47k) N.

Keep in mind that the direction of the forces and their corresponding accelerations affects the direction of the resulting force.