A girl is using a rope to pull a box that weighs 300N across a level surface with constant velocity. The rope makes an angle of 30° above the horizontal, and the tension in the rope is 100 N. What is the normal force of the floor on the box?A 300 N B 86 N C 50 N D 250 N
Question
A girl is using a rope to pull a box that weighs 300N across a level surface with constant velocity. The rope makes an angle of 30° above the horizontal, and the tension in the rope is 100 N. What is the normal force of the floor on the box?A 300 N B 86 N C 50 N D 250 N
Solution
To solve this problem, we need to understand the forces acting on the box.
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First, we have the weight of the box which is acting downwards. This is given as 300N.
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Second, we have the tension in the rope which is pulling the box. This force can be split into two components: one acting vertically upwards and one acting horizontally. The vertical component can be calculated using the sine of the angle the rope makes with the horizontal (since it's opposite to the angle). So, the vertical component of the tension is 100N * sin(30°) = 50N.
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The normal force is the force exerted by the surface to support the weight of the box. When the box is in equilibrium (i.e., moving with a constant velocity), the normal force equals the weight of the box minus the vertical component of the tension in the rope. So, the normal force is 300N - 50N = 250N.
Therefore, the normal force of the floor on the box is 250N, which corresponds to option D.
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