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  1. Problems
  2. /A 20 kg carton of books is at rest on a tiled floor…
HardPhysicsHigh School (9–10)GeneralMechanics › Newton's Laws of MotionNumericalJEE MainBoard ExamAPA-LevelIBAEEE (Amrita)
+23 more exams
AMUEEEAP EAPCETBCECEBITSATCMI EntranceCOMEDK UGETGUJCETIAT (IISER)JCECEJKCETKCETKEAMKIITEELPUNESTMET (Manipal)

A 20 kg carton of books is at rest on a tiled floor…

StemPy LabContributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A 20 kg20\ \text{kg}20 kg carton of books is at rest on a tiled floor. You push it with 80 N80\ \text{N}80 N for 4.0 s4.0\ \text{s}4.0 s, then let go. Friction is 50 N50\ \text{N}50 N while it slides.

A carton of 20 kg on the floor with four arrows: a push of 80 N to the right, friction of 50 N to the left, the normal force up and the weight down.
  1. What is its acceleration while you push?
  2. Its speed and distance when you let go?
  3. How much further does it slide?
  4. The total distance?

Check your answer

Work it out on paper, then type your number. The answer itself stays hidden.

m/s²
m/s
m
m
Need a reminder? The key ideaShowHide

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

Step 1. (a) 80 N−50 N20 kg=1.5 m/s2\dfrac{80\ \text{N} - 50\ \text{N}}{20\ \text{kg}} = 1.5\ \text{m/s}^220 kg80 N−50 N​=1.5 m/s2.

Step 2. (b) v=1.5 m/s2×4 s=6 m/sv = 1.5\ \text{m/s}^2 \times 4\ \text{s} = 6\ \text{m/s}v=1.5 m/s2×4 s=6 m/s; s=12×1.5 m/s2×(4 s)2=12 ms = \tfrac12 \times 1.5\ \text{m/s}^2 \times (4\ \text{s})^2 = 12\ \text{m}s=21​×1.5 m/s2×(4 s)2=12 m.

Step 3. (c) Slowing at 2.5 m/s22.5\ \text{m/s}^22.5 m/s2: (6 m/s)22×2.5 m/s2=7.2 m\dfrac{(6\ \text{m/s})^2}{2 \times 2.5\ \text{m/s}^2} = 7.2\ \text{m}2×2.5 m/s2(6 m/s)2​=7.2 m.

Step 4. (d) 12 m+7.2 m=19.2 m12\ \text{m} + 7.2\ \text{m} = 19.2\ \text{m}12 m+7.2 m=19.2 m.

Answer: 1.5 m/s21.5\ \text{m/s}^21.5 m/s2; 6 m/s6\ \text{m/s}6 m/s and 12 m12\ \text{m}12 m; 7.2 m7.2\ \text{m}7.2 m; 19.2 m19.2\ \text{m}19.2 m.

Check. It slides 7.2 m7.2\ \text{m}7.2 m with no push: moving things do not need a force to keep going.

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