Physics question

Question

A 20kg block of ice that is sitting on the surface of a frozen lake is being pulled by two people (Anna and Elsa) using ropes. (Assume there is no friction.) Anna is pulling the block to the north with a force of 70N. Elsa is pulling the block with a force that has a magnitude of 90N. The direction of Elsa’s pull is towards 60 degrees to the south of east. a. What is the magnitude of the block’s acceleration? b. If the block begins at rest, in which direction will it start moving?

Answer 1

Break the forces up into the components ( North and East or Y and X) and then find the sum of the forces to get acceleration.

Y: Direction

All of Anna's pull at 70 N

only some of Elsa's is in the Y direction

Fy = 70N - sin60 x 90N = 70-77.94 = - 7.94 N

X: Direction

No pulls from Anna, some from Elsa

Fx = 0 + cos60 x 90N = 45 N

The resulting force (That will cause the acceleration) is the result of adding Fx and Fy together:

Magnitude (from a right triangle)

c² = a² + b²

= -7.94² + 45²

= 63.04 + 2025 = 2088.04

so c = Sqrt(2088) = 45.7 N

Use F=ma to get the acceleration. a=F/m = 45.7/20 = 2.28 m/s²

that is the magnitude.

The direction is obtained from the angle between the Fx and Fy vectors.

TanΘ = Fy/Fx = 7.94/45 = .1764

Θ = tan^-1(.1764) = 10 deg

This is 10 degrees South of East