An inventive child wants to reach an apple in a tree without climbing the tree. Sitting in a chair connected to a rope that passes over a frictionless pulley, the child pulls on the loose end of the rope with such a force that the spring scale reads 250 N. The child’s true weight is 320 N, and the chair weighs 160 N. (a) Show that the acceleration of the system is upward and find its magnitude. (b) Find the force the child exerts on the chair.

(a) 0.42 m/s²

(b) 83 N

Explanation:

Assuming g = 10 m/s².

Draw free body diagrams for the child and the chair.

There are three forces on the child:

Tension force T pulling up,

Weight force Mg pulling down,

and normal force N pushing up.

There are three forces on the chair:

Tension force T pulling up,

Weight force mg pulling down,

and normal force N pushing down.

Sum of forces on the child in the y direction:

∑F = ma

T + N − Mg = Ma

Sum of forces on the chair in the y direction:

∑F = ma

T − N − mg = ma

Add the equations together to find the acceleration.

2T − Mg − mg = Ma + ma

a = (2T − Mg − mg) / (M + m)

a = g (2T − Mg − mg) / (Mg + mg)

a = (10 m/s²) (2 × 250 N − 320 N − 160 N) / (320 N + 160 N)

a = 0.42 m/s²

Plug into either equation to find the normal force.

T + N − Mg = Ma

250 N + N − 320 N = (320 N / 10 m/s²) (0.42 m/s²)

N = 83 N

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.

answer: 2×10^-2kg

explanation: density= mass per volume

vol=mass/density

converting to s.i units we have;

3÷1000kg = 0.003

1.5÷100m = 0.15

0.003/0.15 = 0.02kg