A 7.5 kg box is pushed across a floor by pushing forward and down, with a force of 11 N at an angle 64 degrees from the horizontal floor. What is the normal force exerted by the floor onto the box?
Fn = M*g + Fap*sin64. g = 9.8 m/s^2, Fap = 11 N.
Well, it sounds like this box is quite stubborn! I can't even imagine being pushed forward and down at the same time. But anyway, let's calculate the normal force.
First, we need to determine the vertical component of the applied force. We can use trigonometry for that. If we have an angle of 64 degrees and a force of 11 N, the vertical component can be found by multiplying the force by the sine of the angle:
Vertical component = 11 N * sin(64°)
Once we have the vertical component of the applied force, we can calculate the normal force. The normal force is equal to the opposite of the vertical component of the applied force:
Normal force = -Vertical component
So, let's do some math and find out the normal force!
To find the normal force exerted by the floor onto the box, we need to consider the forces acting on the box. In this case, there are two forces: the force applied at an angle and the weight of the box.
1. Resolve the applied force into horizontal and vertical components:
F_horizontal = F_applied * cos(angle)
F_vertical = F_applied * sin(angle)
F_horizontal = 11 N * cos(64°)
F_horizontal ≈ 11 N * 0.4384
F_horizontal ≈ 4.8224 N
F_vertical = 11 N * sin(64°)
F_vertical ≈ 11 N * 0.8968
F_vertical ≈ 9.8648 N
2. Calculate the weight of the box:
Weight = mass * acceleration due to gravity
Weight = 7.5 kg * 9.8 m/s^2
Weight ≈ 73.5 N
3. The normal force is equal to the sum of the vertical component of the applied force and the weight of the box, since the box is on a horizontal floor and not accelerating vertically.
Normal force = F_vertical + Weight
Normal force ≈ 9.8648 N + 73.5 N
Normal force ≈ 83.3648 N
Therefore, the normal force exerted by the floor onto the box is approximately 83.3648 N.
To find the normal force exerted by the floor onto the box, we need to consider the forces acting on the box in the vertical direction.
First, let's resolve the given force into its vertical and horizontal components.
Vertical component of force = force * sin(angle)
Vertical component of force = 11 N * sin(64 degrees)
Vertical component of force = 11 N * 0.8988
Vertical component of force ≈ 9.887 N
Now, since the box is on a horizontal floor and not accelerating vertically, the normal force exerted by the floor onto the box is equal in magnitude to the weight of the box.
Weight of the box = mass * acceleration due to gravity
Weight of the box = 7.5 kg * 9.8 m/s^2
Weight of the box = 73.5 N
Therefore, the normal force exerted by the floor onto the box is approximately 73.5 Newtons.