A 15 kg box is given an initial push to start it moving up a frictionless ramp with angle theta = 30 degree and length delta r = 22m. What horizontal force F will keep the box moving with constant speed to the top of the ramp?
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M*g = 15 * 9.8 = 147 N. = Wt. of
box.
Fp = 147*sin30 = 73.5 N. = Force parallel to the incline.
Fx = Fp*Cos30 = 73.5*Cos30 = 63.6 N.
To find the horizontal force required to keep the box moving with constant speed up the ramp, we need to consider the forces acting on the box.
First, let's analyze the forces acting parallel to the ramp. Since the ramp is frictionless, the only force in this direction is the component of the weight of the box acting parallel to the ramp surface. We can find this force using trigonometry.
The weight of the box is given by the formula:
Weight = mass * gravity
where mass is 15 kg and gravity is approximately 9.8 m/s^2.
Weight = 15 kg * 9.8 m/s^2
Weight = 147 N
Now, let's find the component of the weight along the ramp. This can be calculated using trigonometry. The component of the weight parallel to the ramp (F_parallel) is given by:
F_parallel = weight * sin(theta)
where theta is the angle of the ramp, which is 30 degrees in this case.
F_parallel = 147 N * sin(30 degrees)
F_parallel = 73.5 N
Since the box is moving with constant speed, the force required to counteract the component of the weight parallel to the ramp is equal in magnitude, but opposite in direction. Therefore, the horizontal force (F) required to keep the box moving with constant speed up the ramp is also 73.5 N.
In summary, the horizontal force (F) required to keep the box moving with constant speed up the ramp is 73.5 N.