{"id":24557,"date":"2025-06-18T16:08:43","date_gmt":"2025-06-18T16:08:43","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=24557"},"modified":"2025-06-18T16:08:45","modified_gmt":"2025-06-18T16:08:45","slug":"a-73-8-kg-person-stands-on-a-scale-in-an-elevator","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-73-8-kg-person-stands-on-a-scale-in-an-elevator\/","title":{"rendered":"A 73.8-kg person stands on a scale in an elevator"},"content":{"rendered":"\n

A 73.8-kg person stands on a scale in an elevator. What is the apparent weight when the elevator is (a) accelerating upward with an acceleration of 1.85 m\/s^2, (b) moving upward at a constant speed, and (c) accelerating downward with an acceleration of 1.49 m\/s^2?<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To determine the apparent weight<\/strong> of a person in an elevator, we must consider the effect of the elevator’s motion on the normal force<\/strong> the scale reads. Apparent weight is essentially the normal force NNN acting on the person. The actual weight is the force due to gravity, given by:W=mgW = mgW=mg<\/p>\n\n\n\n

where
m=73.8\u2009kgm = 73.8 \\, \\text{kg}m=73.8kg (mass of the person)
g=9.8\u2009m\/s2g = 9.8 \\, \\text{m\/s}^2g=9.8m\/s2 (acceleration due to gravity)<\/p>\n\n\n\n

\n\n\n\n

Step-by-step Calculations<\/h3>\n\n\n\n

Actual weight:<\/h4>\n\n\n\n

W=73.8\u00d79.8=723.24\u2009NW = 73.8 \\times 9.8 = 723.24 \\, \\text{N}W=73.8\u00d79.8=723.24N<\/p>\n\n\n\n

\n\n\n\n

(a) Elevator accelerating upward<\/strong> with a=1.85\u2009m\/s2a = 1.85 \\, \\text{m\/s}^2a=1.85m\/s2<\/h3>\n\n\n\n

When accelerating upward, the apparent weight increases because the normal force must not only balance gravity but also provide upward acceleration:N=m(g+a)=73.8\u00d7(9.8+1.85)=73.8\u00d711.65=859.47\u2009NN = m(g + a) = 73.8 \\times (9.8 + 1.85) = 73.8 \\times 11.65 = 859.47 \\, \\text{N}N=m(g+a)=73.8\u00d7(9.8+1.85)=73.8\u00d711.65=859.47N<\/p>\n\n\n\n

Apparent weight = 859.47 N<\/strong><\/p>\n\n\n\n

\n\n\n\n

(b) Elevator moving upward at constant speed<\/strong><\/h3>\n\n\n\n

At constant speed, acceleration is zero. The only force to balance is gravity:N=mg=73.8\u00d79.8=723.24\u2009NN = mg = 73.8 \\times 9.8 = 723.24 \\, \\text{N}N=mg=73.8\u00d79.8=723.24N<\/p>\n\n\n\n

Apparent weight = 723.24 N<\/strong><\/p>\n\n\n\n

\n\n\n\n

(c) Elevator accelerating downward<\/strong> with a=1.49\u2009m\/s2a = 1.49 \\, \\text{m\/s}^2a=1.49m\/s2<\/h3>\n\n\n\n

When accelerating downward, the apparent weight decreases:N=m(g\u2212a)=73.8\u00d7(9.8\u22121.49)=73.8\u00d78.31=613.28\u2009NN = m(g – a) = 73.8 \\times (9.8 – 1.49) = 73.8 \\times 8.31 = 613.28 \\, \\text{N}N=m(g\u2212a)=73.8\u00d7(9.8\u22121.49)=73.8\u00d78.31=613.28N<\/p>\n\n\n\n

Apparent weight = 613.28 N<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation<\/h3>\n\n\n\n

In all cases, the apparent weight is determined by the net acceleration<\/strong> experienced by the person. When accelerating upward, the scale must push harder, making the reading higher. When moving at a constant velocity, only gravity acts. When accelerating downward, the scale pushes less, so the reading drops. This principle is rooted in Newton\u2019s Second Law of Motion F=maF = maF=ma, where the direction and magnitude of acceleration change the required normal force.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

A 73.8-kg person stands on a scale in an elevator. What is the apparent weight when the elevator is (a) accelerating upward with an acceleration of 1.85 m\/s^2, (b) moving upward at a constant speed, and (c) accelerating downward with an acceleration of 1.49 m\/s^2? The Correct Answer and Explanation is: To determine the apparent […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-24557","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/24557","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=24557"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/24557\/revisions"}],"predecessor-version":[{"id":24562,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/24557\/revisions\/24562"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=24557"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=24557"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=24557"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}