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Answer :
Final answer:
To find the force applied to the suitcase's handle, we use Newton's second law and force components, calculating it as 91.2 N.
Explanation:
To find the force F applied to the handle of the 22 kg suitcase being pulled at a constant speed with a handle angle of 30° above the horizontal, we can use the concepts of Newton's second law and components of force. Given that the normal force (N) is 170 N, we first need to understand that the weight (W) of the suitcase acts downward and is equal to the mass multiplied by the acceleration due to gravity (g = 9.8 m/s2). The normal force is the component of the force perpendicular to the surface, and it counters part of the weight of the suitcase. However, because the handle is pulled at an angle, part of the force applied (F) also acts upwards against the weight, reducing the normal force.
First, calculate the weight of the suitcase: W = m × g = 22 kg × 9.8 m/s2 = 215.6 N.
Then, knowing that the normal force and the vertical component of the applied force together balance the weight, we can write: N + Fy = W. Here, Fy is the vertical component of the applied force F, which can be found using trigonometry: Fy = F × sin(θ), where θ is the angle of the handle with the horizontal.
To find F, rearrange the formula to solve for F: F = (W - N) / sin(θ). Plugging in the values gives us: F = (215.6 N - 170 N) / sin(30°) = (45.6 N) / 0.5 = 91.2 N. Therefore, the force applied to the handle is 91.2 N.
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