im not completely sure im right with this question
a lawn spreader is pushed across a lawn by applying a force of 95N along the handle that makes an angle 60 degrees with the horizontal. a- what is the horiz. and vert. comp. of the force. b- when the handle is lowered to 30 degrees with the horiz., calc. the vert. and horiz. comp. of the force.
for a i got:
95 cos60 (which is -90.479)
and
95 sin60 (which is -28.957)
is that right?
and for b i got:
95 cos30 (which is 14.65)
and
95 sin30 (which is -93.86)
is that right?..
Those answers are incorrect. I think I know what you are doing wrong. Remember that the angles are in DEGREES, not radians. cos 60 is 0.500 and sin 60 is 0.86603. You have apparently been using a calculator that has been set to accept angles in radians, not degrees. Hand calculators usually have a button operation that lets you switch from degrees to radians when using the trig functions.
To solve this question, you are correct in using trigonometric functions to find the horizontal and vertical components of the force applied.
For part a, the force of 95N is applied at an angle of 60 degrees with the horizontal. To find the horizontal component, you multiply the force by the cosine of the angle:
Horizontal component = 95N * cos(60 degrees) ≈ -90.479N
To find the vertical component, multiply the force by the sine of the angle:
Vertical component = 95N * sin(60 degrees) ≈ 82.248N
However, it seems like you made a sign error in your calculations. The horizontal component should be positive and the vertical component should be negative. So the correct results are:
Horizontal component = 95N * cos(60 degrees) ≈ 47.5N
Vertical component = -95N * sin(60 degrees) ≈ -82.248N
For part b, the angle is now 30 degrees with the horizontal. You can use the same approach to find the horizontal and vertical components:
Horizontal component = 95N * cos(30 degrees) ≈ 82.248N
Vertical component = -95N * sin(30 degrees) ≈ -47.5N
Again, it seems like you made a sign error in your calculations. The horizontal component should be positive and the vertical component should be negative. So the correct results are:
Horizontal component = 95N * cos(30 degrees) ≈ 82.248N
Vertical component = -95N * sin(30 degrees) ≈ -47.5N
Therefore, your calculations for part b are incorrect. The correct answers are:
Horizontal component = 82.248N
Vertical component = -47.5N