a force of 372
N is used to move a piano with a maass of 532 kg up a ramp 14 m long. what is the vertical height of the ramp
Do you have any thoughts, or do you have any work to show for this question? Where do you get stuck?
M*g = 532 * 9.6 = 5214 N. = Wt. of piano.
Work = F*d = 372 * 14 = 5208 J.
PE = Mg*h = 5208.
5214h = 5208, h = 1.0 m.
To find the vertical height of the ramp, you can use the concept of work done.
Work is defined as the force applied in the direction of motion multiplied by the distance traveled. In this case, the force applied is 372 N and the distance traveled is 14 m.
However, since the piano is being moved up the ramp, only a fraction of the total distance traveled is in the vertical direction. The rest of the distance is along the inclined ramp.
To find the vertical height, we need to calculate the vertical component of the distance traveled. This can be done using a trigonometric function called sine.
First, we need to find the angle of inclination of the ramp. This can be determined using the formula:
sin(angle) = vertical height / length of the ramp
Rearranging the formula, we get:
angle = arcsin(vertical height / length of the ramp)
Now, we can use the Sine Rule:
sin(angle) = opposite / hypotenuse
In this case, the hypotenuse is the length of the ramp (14 m) and the opposite side is the vertical height we need to find.
Rearranging the formula, we get:
vertical height = sin(angle) * length of the ramp
To find the angle, we can use the equation:
angle = arcsin(vertical height / length of the ramp)
Plugging in the values, we have:
angle = arcsin(vertical height / 14)
To solve for the vertical height, we need to rearrange the formula:
vertical height = angle * 14
To calculate the angle, we can use the inverse sine function on a scientific calculator or an online tool, and then substitute it into the formula to find the vertical height.