If the 1 kg standard body has an acceleration of 2.00 m/s2 at 20.0° to the positive direction of an x axis, what are (a) the x component and (b) the y component of the net force acting on the body, and (c) what is the net force in unit-vector notation?
a) Fx = M * 2.00 cos 20 m/s^2 = 18.79 n
b) Fy = M * 2.00 sin 20 m/s^2 = 6.82 n
c) Fx i + Fy j
i and j are unit vectors
2. If the 1 kg standard body has anacceleration of 2.00m/s3 at 20% to the positive direction of an x axis, what are a the x component and (b) the y component of the net force acting on the body, and c) what is the net force in rectornotation?
Does M represent gravity ?
A 2.00 kg object is subjected to three forces that give acceleration ( ) ( )j sms ima rrr 22 /6/8 += − . If two of the three forces are ( ) ( )j NN iF rrr 16.030.01 += and ( ) ( )j NN iF rrr 8.012.02 += − , find the third force.
To find the x and y components of the net force acting on the body, we need to use trigonometry and Newton's second law.
First, let's break down the given information:
- Mass (m) = 1 kg
- Acceleration (a) = 2.00 m/s²
- Angle (θ) = 20.0°
To determine the x and y components, we can apply the following equations:
(a) x component of net force (Fₓ):
Fₓ = m * a * cos(θ)
(b) y component of net force (Fᵧ):
Fᵧ = m * a * sin(θ)
Now let's calculate the x and y components:
(a) x component of net force (Fₓ):
Fₓ = 1 kg * 2.00 m/s² * cos(20.0°)
To calculate the cosine of 20.0°, you can use a scientific calculator or lookup table. The cosine of 20.0° is approximately 0.9397.
Fₓ = 1 kg * 2.00 m/s² * 0.9397
(b) y component of net force (Fᵧ):
Fᵧ = 1 kg * 2.00 m/s² * sin(20.0°)
To calculate the sine of 20.0°, you can use a scientific calculator or lookup table. The sine of 20.0° is approximately 0.3420.
Fᵧ = 1 kg * 2.00 m/s² * 0.3420
(c) Net force in unit-vector notation:
The net force can be expressed in unit-vector notation as the sum of its x and y components:
Net force (F) = Fₓ * î + Fᵧ * ĵ
Where î and ĵ represent the unit vectors in the x and y directions respectively.
Now you can substitute the calculated values into the equation to get the net force in unit-vector notation.
Note: Remember to include the appropriate units in your final answer.