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
Wb = mg = 66kg * 9.8N/kg = 647 N. =
Wt. of box.
Fb = 647 N. @ 30 Deg. = Force of box.
Fp = 647*sin30 = 323.5 N. = Force parallel to ramp.
Fv = 647*cos30 = 560.3 N. = Force perpendicular to ramp.
Fk = u * Fv = 0.35 * 560.3 = 196.1 N. =
Force of kinetic friction.
Fn = Fap - Fp - Fk = 0, a = 0.
Fap - 323.5 - 196.1 = 0,
Fap - 519.6 = 0,
Fap = 519.6 N. = Force applied.
To determine the magnitude of the force parallel to the ramp needed to move the box up the ramp at a constant speed, we need to consider the forces acting on the box.
There are two main forces to consider here: the force of gravity acting vertically downward and the force of kinetic friction acting parallel to the ramp.
1. Force of gravity: This force can be calculated using the formula F = mg, where m is the mass of the box (66 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²). Thus, the force of gravity is F_gravity = (66 kg) x (9.8 m/s²).
2. Force of kinetic friction: This force can be determined by multiplying the coefficient of kinetic friction (0.35) by the normal force, which is the component of the force of gravity perpendicular to the ramp. The normal force can be calculated as the product of the mass of the box and the cosine of the angle of the ramp (30°). Therefore, the normal force is F_normal = (66 kg) x (9.8 m/s²) x cos(30°). The force of kinetic friction is F_friction = (0.35) x F_normal.
Now, since we want the box to move up the ramp at a constant speed (which means the net force must be zero), the force parallel to the ramp that we need to exert must be equal to the force of kinetic friction. Therefore, the magnitude of the force parallel to the ramp that we should push on the box is equal to the force of kinetic friction: F_push = F_friction = (0.35) x F_normal.
To calculate the numerical value, you can substitute the values of the mass, coefficient of kinetic friction, gravity, and angle into the equations and perform the necessary calculations.
Once you have determined the value of F_push, you can provide it in newtons (N) as requested.