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Chapter 7: Q. 24 (page 178)

The 1.0kgblock in FIGURE EX7.24is tied to the wall with a rope. It sits on top of the 2.0kgblock. The lower block is pulled to the right with a tension force of 20N. The coefficient of kinetic friction at both the lower and upper surfaces of the 2.0kgblock is 渭k=0.40

a. What is the tension in the rope attached to the wall?

b. What is the acceleration of the 2.0kgblock?

Short Answer

Expert verified

(a) The tension in the rope attached to the wall is 3.92N

(b) The acceleration of the2kgblock.

Step by step solution

01

Given information (part a)

Mass of lower block, M=2kg

Mass of the upper block, m=1kg

External force Fext=20N

Coefficient of kinetic friction渭k=0.4

02

Explanation (part a)

The tension in the rope will be equal to frictional force acting on 1 kg mass.

T=渭kmgm=1kgg=9.8m/s2T=0.41kg9.8m/s2=3.92N

The tension in the rope is3.92N

03

Given information (part b)

Mass of lower block,M=2kg

Mass of the upper block,m=1kg

External forceFext=20N

Coefficient of kinetic friction渭k=0.4

04

Explanation (part b)

Frictional force at the upper and lower surface of 2 kg block will try to prevent its motion.

The equation of motion of 2 kg block is as follows.

Ma=Fa-T-fkwherefk=渭km+MgMa=Fa-T-渭km+Mg2kga=20N-3.92N-0.41kg+2kg9.8m/s22kga=4.32Na=4.32N2kga=2.16m/s2

The acceleration of the 2kgblock is 2.16m/s2

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Most popular questions from this chapter

A 3200kghelicopter is flying horizontally. A 250kgcrate is suspended from the helicopter by a massless cable that is constantly 20掳from vertical. What propulsion force F u prop is being provided by the helicopter鈥檚 rotor? Air resistance can be ignored. Give your answer in component form in a coordinate system where i^points in the direction of motion and j^points upward.

FIGUREP7.39shows a block of mass m resting on a 20掳slope. The block has coefficients of friction渭s=0.80 and渭k=0.50 with the surface. It is connected via a massless string over a massless, frictionless pulley to a hanging block of mass 2.0kg.

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A 50-cm-diameter, 400 g beach ball is dropped with a 4.0 mg ant riding on the top. The ball experiences air resistance, but the ant does not. What is the magnitude of the normal force exerted on the ant when the ball鈥檚 speed is 2.0 m/s?

You find yourself in the middle of a frozen lake with a surface so slippery 渭s=渭k=0 you cannot walk. However, you happen to have several rocks in your pocket. The ice is extremely hard. It cannot be chipped, and the rocks slip on it just as much as your feet do. Can you think of a way to get to shore?Use pictures, forces, and Newton's laws to explain your reasoning.

What is the acceleration of the 3.0kgblock in FIGURECP7.55across the frictionless table?

Hint: Think carefully about the acceleration constraint.
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