Question

A 4-meter plank weighing 7 kg is lying on a dock with 3.14 meters of its length on the dock, and the rest of its length extending off the dock. If a child weighing 69 kg walks out onto the part of the plank extending off the dock, what is the maximum distance in meters that the child can walk on the plank from the edge of the dock before he falls into the water?

A baseball pitcher throws a 157 g baseball at a velocity of 31 m/s towards home plate. The batter hits the ball, and the velocity of the ball coming off the bat is 52 m/s in the opposite direction of the velocity of the pitch. The bat is in contact with the ball for 0.003 seconds. What is the magnitude in Newtons of the average force applied to the ball?

Answer 1

0 m2 ча x= maximum distance, Torque about a =D ong. x= mg =) 69xx - 7x1114 14. 0.16 force 6 rate of change in momentum fata de (v2) - (m (-)) - ml vetve) -) E= 157x10 3 x (52 +31) 0.003 F=4343.6 N.

Answer 2

ONLY ANSWER FOR QUESTION 1

Mass of plank = 7kg

Plank total length = 4m

Length of plank on dock = 3.14m

Mass of child = 69kg

Equation to work with:

F1 * d1 = F2 * d2

To find F1, you must multiply the mass of the plank by the earth's gravitational pull, 9.81m/s^2, to find the force that would be opposing the child's force...

F1 = m1 * g

F1 = 7kg * 9.81m/s^2

F1 = 68.67 N

To find d1, you must first know that the plank's center of mass is right in the middle at 2m. With 3.14m of the plank being on the dock, we must find the moment of the mass where the 7kg acts. To find this...

3.14m - 2m = 1.14m

(Length of plank on the dock - length of 1/2 the plank = how far the point the mass is acting is from the edge of the dock, where the plank is hanging off.)

To find F2, you must multiply the mass of the child by the earth's gravitational pull, 9.81m/s^2, to find the force that would be opposing the force of the part of the plank on the dock...

F2 = m2 * g

F2 = 69kg * 9.81m/s^2

F2 = 676.89 N

Now, you plug in your values to solve for the variable, d2.

F1 * d1 = F2 * d2

68.67N * 1.14m = 676.89N * d2

Solve for d2.

d2 = 0.11565 meters