You want to push a 66-kg box up a 30° ramp. The coefficient of kinetic friction between the ramp and the box is 0.35. With what magnitude force parallel to the ramp should you push on the box so that it moves up the ramp at a constant speed?
N
Physics - bobpursley, Thursday, February 16, 2012 at 5:04pm
You have to overcome friction and gravity
gravity down the plane:mg*SinTheta
friction: mg*mu*cosTheta
I know i posted this before earlier sorry about that but I really need help with it because its not working out please help
Hello! You have the correct formula: F= mgsin theta
Now plug in those values!
m=66 kg
g= 9.8 m/s^2
theta (angle)= 30 degrees
Normal Force= 66 * 9.8 * 0.5
Normal Force= 33 * 9.8
Normal Force= 323.4 Newtons
Then, use F=coefficient of friction * Normal Force
F= 0.35 * 323.4
F=113.19 Newtons which rounds to 113.2 N
Hope this helps!
To find the magnitude of the force parallel to the ramp required to push the box up at a constant speed, we need to consider the forces acting on the box.
1. Weight: The force due to gravity is acting vertically downward and can be calculated as the mass of the box (m) multiplied by the acceleration due to gravity (g). In this case, the weight component acting down the ramp is mg * sin(theta), where theta is the angle of the ramp.
2. Friction: The force of friction opposes the motion of the box and can be calculated as the product of the coefficient of kinetic friction (mu) and the normal force (N). The normal force is the force perpendicular to the ramp, and in this case, it is equal to mg * cos(theta).
To keep the box moving at a constant speed, the force pushing the box up the ramp (parallel force) must be equal to the combined effect of gravity down the ramp and the force of friction.
Therefore, the force parallel to the ramp can be calculated as:
Force_parallel = Weight down the ramp + Friction
Force_parallel = (mg * sin(theta)) + (mu * (mg * cos(theta)))
Substituting the given values:
Mass (m) = 66 kg
Coefficient of kinetic friction (mu) = 0.35
Angle of the ramp (theta) = 30°
Acceleration due to gravity (g) = 9.8 m/s²
Force_parallel = (66 kg * 9.8 m/s² * sin(30°)) + (0.35 * (66 kg * 9.8 m/s² * cos(30°)))
Calculating the above expression:
Force_parallel = (66 * 9.8 * 0.5) + (0.35 * (66 * 9.8 * 0.866))
Force_parallel = 323.4 N + 202.5 N
Force_parallel = 525.9 N
Therefore, to keep the box moving up the ramp at a constant speed, a force of magnitude 525.9 N parallel to the ramp should be applied.