A contestant in a winter games event pushes a 43.0 kg block of ice across a froz

Question

A contestant in a winter games event pushes a 43.0 kg block of ice across a frozen lake as shown in Figure 4.29(a). The coefficient of static friction is 0.1 and the coefficient of kinetic friction is 0.03.

(a) Calculate the minimum force F he must exert to get the block moving.

(b) What is its acceleration once it starts to move, if that force is maintained?

A contestant in a winter games event pushes a 43.0 kg block of ice across a frozen lake as shown in Figure 4.29(a). The coefficient of static friction is 0.1 and the coefficient of kinetic friction is 0.03. Calculate the minimum force F he must exert to get the block moving. What is its acceleration once it starts to move, if that force is maintained?

Explanation / Answer

Let F be the force applied to the block
The normal force of the lake ice on the block is

Fn = Fsin? + mg

The friction force before sliding is
Ff = ?Fn
Ff = ?(Fsin? + mg)

so the force needed to begin to displace the block is(using the static friction coefficient) is equal to the friction force

But we also know from geometry that

Fh = Fcos?

so

Fcos? = ?(Fsin? + mg)
Fcos? = ?Fsin? + ?mg
Fcos? - ?Fsin? = ?mg
F(cos? - ?sin?) = ?mg
F = ?mg / (cos? - ?sin?)

F = 0.1(43)9.81 / (cos25 - 0.1sin25)

F = 48.82 N


Now with a force of 48.82 N what is the acceleration with coefficient of friction at 0.03

so the net force Fa accelerating the block is the total horizontal force minus the friction force

Fa = Fh - Ff
Fa = Fcos? - ?(Fsin? + mg)

as Fa = ma

ma = Fcos? - ?(Fsin? + mg)
a = Fcos? - ?(Fsin? + mg) / m

a = (48.82cos25 - 0.03(48.82sin25 + 43(9.81))) / 43
a = 0.72 m/s

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