Pual is trying to push a heavy box W on the ground, but he can’t. The graph belo

Question

Pual is trying to push a heavy box W on the ground, but he can’t. The graph below shows the direction he applies his force. The angle is equal to 30 degrees . The force from Paul is roughly 150N. Let’s assume the box is 50kg and the static friction coefficient is 0.3. Please answer the following questions.

1) how large is the friction?

2) how large is the force needed in order to make the box move?

3) Paul can actually push the box without increasing the force, what should he do? (Hint: consider the direction of the force. There are more than one way to do it. Use your calculation to show that he can move the box. )

Explanation / Answer

here,

writing F in terms of comonents

Px = Pcos30 = 150 * 0.86 = 129 N
Py = Psin30 = 150 * 0.5 = 75 N

Force due to gravity
Fg = mg = 50*9.8
Fg= Normal force on block = 490 N

Part a:
Frictinal force wil be

Ff = uN = 0.3*490 = 147 N

part b:
for the box to moved, force needed

Fnet = Ff - Px = 147 - 129 = 18 N

he need 18N more force in horizantal direction to move the box

Part c:

he can try appling force at angle 0 degress, as at that moment Horizontal force will be maximum as shown

Px = 150cos0 = 150 *1 = 150N

which is greater than Ff ,so the box will just move

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