a mover uses a ramp to pull a 1000 newton cart up to the floor of his truck 0.8 meters high if it takes a force or 200 newtons to pull the cart what is the length of the ramp
Graham is partially right. MA= LOAD/EFFORT which gives you 1000N/200N = 5. 200N/1000N= 0.2. So now, 5 = length / 0.8m. Multiply both sides by 0.8m in order to isolate length. 5 x 0.8m = length = 4m
4m
First, calculate the Mechanical Advantage by using MA = effort / load where effort is 200N (using 200N of effort to pull the cart) and load is 1000N (the cart exerts a force of 1000N on the ramp - the ramps load). 200N / 1000N = 5. Then use the ideal mechanical advantage formula for a ramp: IMA = length / height where IMA is the MA that we just calculated - 5, and height is 0.8m. Set up the equation like this: 5 = length / 0.8m = 4m
The answer depends upon the amount of friction. If there is no friction, they should have said so.
In the frictionless case,
(Force) x (ramp length) = (weight) x (height)
To approximate frictionless behavior, the cart should have well lubricated wheels.
To find the length of the ramp, we can use the concept of work. Work is defined as the force applied to an object multiplied by the distance over which the force is applied.
In this scenario, the force applied to pull the cart is 200 newtons, and the distance over which the force is applied is the height of the ramp, which is 0.8 meters.
Work = Force x Distance
Therefore, we can calculate the work done to pull the cart:
Work = 200 N x 0.8 m
Work = 160 joules
Now, we know that the work done is equal to the force multiplied by the distance:
Work = Force x Distance
160 joules = 1000 N x Ramp length
To find the length of the ramp, we rearrange the equation:
Ramp length = 160 joules / 1000 N
Ramp length = 0.16 meters
Therefore, the length of the ramp required to pull the 1000 newton cart with a force of 200 newtons to the floor of the truck 0.8 meters high is 0.16 meters.