A 115.0 kg box is pushed by a horizontal force F at constant speed up a frictionless ramp which makes an angle of 46.0 deg with the horizontal. Find the magnitude of the applied force F. what is the magnitude of the normal force between the ramp and the box?
m*g = 115 * 9.8 = 1127 N. = Wt of box.
Fp = 1127*sin46 = 810.7 N. = Force
parallel to the ramp.
F-Fp = m*a
F - 810.7 = m*0 = 0
F = 810.7 N.
Fn = 1127*cos46 = 782.9 N. = Normal
force.
That's wrong
Correction:
F*cosA-Fp = m*a
F*cos46-810.7 = m*0 = 0
F*cos46 = 810.7
F = 1167 N.
To find the magnitude of the applied force, we can start by analyzing the forces acting on the box.
1. Gravitational force (weight): The weight of the box can be calculated by multiplying the mass (115.0 kg) by the acceleration due to gravity (9.8 m/s^2). Therefore, the weight of the box is (115.0 kg) x (9.8 m/s^2) = 1127 N.
2. Normal force (perpendicular to the ramp): The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, it is the force exerted by the ramp on the box perpendicular to the ramp's surface. Because the box is at constant speed, the normal force must be equal in magnitude and opposite in direction to the gravitational force (weight). Therefore, the normal force is also 1127 N.
3. Applied force: The applied force is the force applied to the box to push it up the ramp. Since the box is moving at a constant speed, the applied force must exactly balance the gravitational force (weight), resulting in no net force acting on the box. Therefore, the magnitude of the applied force is also 1127 N.
In summary, the magnitude of the applied force (F) and the magnitude of the normal force between the ramp and the box are both 1127 N.