If a 1.00 kg body has an acceleration of 3.69 m/s2 at 75° to the positive direction of the x axis, then what are (a) the x component and (b) the y component of the net force on it, and (c) what is the net force in unit-vector notation?
If f = ma can f = 2, am I on the right track to solving?
x component:
Fx = M a cos75
y component:
Fy = m a sin75
Net force: Fx*i + Fy*j
Yes, you are on the right track to solving the problem using the equation F = ma. In this equation, F represents the net force acting on an object, m represents the mass of the object, and a represents the acceleration of the object.
Let's break down the problem into parts.
(a) To find the x component of the net force on the body, we need to use the following equation:
F_x = F * cosθ
where F_x is the x component of the net force, F is the magnitude of the net force, and θ is the angle between the net force and the positive direction of the x-axis. In this case, the angle θ is given as 75°.
Given that the acceleration of the body is 3.69 m/s^2, we can substitute this value for a (acceleration) in the equation. However, we still need to find the net force F. To find F, we can rearrange the equation as:
F = m * a
Given that the mass of the body is 1.00 kg, we substitute this value for m in the equation. Now we have both F and a, so we can go ahead and calculate F_x.
(b) To find the y component of the net force on the body, we use a similar equation:
F_y = F * sinθ
where F_y is the y component of the net force.
(c) Finally, to express the net force in unit-vector notation, we can write it as:
F_net = F_x * î + F_y * ĵ
where î represents the unit vector in the x-direction and ĵ represents the unit vector in the y-direction.
By following these steps, you can find the x component, y component, and the net force of the given problem.