4. the fire alarm goes off, and a 97 kg fireman slides 3.0 m down a pole to the ground floor. suppose the fireman starts from rest, slides with a constant acceleration, and reaches the ground floor in 1.2 s. (a) what was the upward force f exerted by the pole on the fireman

The upward force F was 546.11 N

Explanation:

In order to find the value of the force F, you have to apply Newton's Second Law:

∑F=ma

where F represents all the forces, m is the mass and a is the acceleration.

In this case, the applied forces are the force F exerted by the pole and the weight force, due to the acceleration of gravity.

Replacing in the formula the components of the forces in the y-axis:

Using a positive direction downward:

-F + W = ma

-F + mg=ma

F = mg - ma (I)

Notice that F is upward and the weight is downward.

You need to calculate the acceleration with the given information and then you can calculate the value of F.

Applying kinematic motion formula:

Yf= Yo+ Vot + 0.5at²

where yo is the initial position, vo is the initial velocity, a is the acceleration, t is the time and Yf is the final position.

In this case:

t=1.2s

vo=0 (because the fireman starts from rest)

Yo= 0 m  and Yf= 3.0 m

Therefore:

3.0 = 0 + 0(1.2) + 0.5a(1.2)²

3.0 = 0.72a

Dividing by 0.72

a = 4.17 m/s²

Replacing it in (I):

F= 97(9.8) - 97(4.17)

F = 546.11 N

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jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.