Question

Your little sister wants a ride on her sled.If you are on flat ground ,should you push her or pull her ?Specify the reason. Assume the same angle in each case.

Answer 1

Your little sister wants a ride on her sled

Case A: When you're pushing her, then From FBD (A)

Using force balance in vertical direction:

Fy_net = N - F*sin - W

Since sled is not moving in vertical direction, So

Fy_net = 0

N = F*sin + W

Now using force balance in horizontal direction:

Fx_net = F*cos - Ff

Ff = kinetic friction force (Assuming = Coefficient of kinetic friction)

Ff = *N = *(F*sin + W)

Fx_net = m*a (From newton's 2nd law)

W = Weight of your sister = m*g

So,

m*a = F*cos - *(F*sin + m*g)

F*(cos - *sin ) = m*a + *m*g

F = Force required to push = m*(a + *g)/(cos - *sin )

Case B: When you're Pulling her, then From FBD (B)

Using force balance in vertical direction:

Fy_net = N + F*sin - W

Since sled is not moving in vertical direction, So

Fy_net = 0

N = W - F*sin

Now using force balance in horizontal direction:

Fx_net = F*cos - Ff

Ff = kinetic friction force (Assuming = Coefficient of kinetic friction)

Ff = *N = *(W - F*sin )

Fx_net = m*a (From newton's 2nd law)

W = Weight of your sister = m*g

So,

m*a = F*cos - *(m*g - F*sin )

F*(cos + *sin ) = m*a + *m*g

F = Force required to pull = m*(a + *g)/(cos + *sin )

Step 2:

F1 = Force required to push = m*(a + *g)/(cos - *sin )

F2 = Force required to pull = m*(a + *g)/(cos + *sin )

Compare F1 and F2

since (cos + *sin ) is always greater than (cos - *sin ), So

F2 will always be lower than F1

So F2 < F1

Which means it is easier to pull, So you should pull her

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