Answer:
66.4 N
Explanation:
From Newton's second law, F = ma
where F is the force, m is the mass and a is the acceleration.
Because the object has acceleration in two directions and the mass is constant, the force will be in two directions. The component of the forces are:
[tex]F_x = ma_x = (7.00\text{ kg})(3.00 \text{ m/s}^2) = 21.0\text{ N}[/tex]
[tex]F_y = ma_y = (7.00\text{ kg})(9.00 \text{ m/s}^2) = 63.0\text{ N}[/tex]
The magnitude of the resultant force is given by
[tex]F = \sqrt{F_x^2+F_y^2}[/tex]
[tex]F = \sqrt{(21.0\text{ N})^2+(63.0\text{ N})^2} = \sqrt{(441.0\text{ N}^2)+(3969.0\text{ N}^2)} = \sqrt{(4410\text{ N}^2)} = 66.4 \text{ N}[/tex]
Answer:
(a) Fx = 21 N, Fy = 63 N
(b) 66.41 N
Explanation:
(a)
Note: the components of the force acting on the object is the force acting on the horizontal axis (Fx) as well as the vertical axis (Fy)
Fx = m(ax).............................. Equation 1
Where Fx = Horizontal force acting on the object, m = mass of the object, ax = acceleration of the object in the horizontal axis.
Given: m = 7 kg, ax = 3.0 m/s²
Substitute into equation 1
Fx = 7(3)
Fx = 21 N.
Similarly,
For the y- axis,
Fy = may.......................... Equation 2
Where Fy = vertical force acting on the object, m = mass of the object, ay = Vertical acceleration of the object
Given: m = 7 kg, ay = 9.0 m/s²
Substitute into equation 2
Fy = 7(9)
Fy = 63 N.
(b)
Assuming the horizontal and the vertical force are at right angle,
Using Pythagoras theorem,
Fr = √(Fx²+Fy²).................... Equation 3
Where Fr = magnitude of the resultant force
Given: Fx = 21 N, Fy = 63 N
Substitute into equation 3
Fr = √(21²+63²)
Fr = √(441+3969)
Fr = √(4410)
Fr = 66.41 N.
Hence the magnitude of the resultant force = 66.41 N
