A student pulls a block over a rough surface with a constant force FP that is at an angle θ above the horizontal, as shown above. If FP remains constant but the angle θ is increased, which of the following is true at some later time?

A. The force of friction between the block and surface will increase.

B. The force of friction between the block and surface will decrease.

C. The weight of the block will increase.

D. The weight of the block will decrease.

Here, we are required to identify which of the statements is true.

The statement which is true is Choice B:

The force of friction between the block and surface will decrease.

Since, the force of friction is given by

F =μN

where μ is the coefficient of friction and N is the normal force.

The force of pull with which the student pulls the block is given as; Fp

which subtends an angle θ with the horizontal, the normal force on the block becomes

N = (Mg- Fpsinθ).

and consequently, the frictional force becomes

Fs = μ(Mg- Fpsinθ)

Therefore, upon increasing θ , sinθ increases which consequently decreases the normal force, N = (Mg - Fpsinθ) , which also means the frictional force decreases.

Evidently, choice B is true..

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B.The force of friction between the block and surface will decrease.

Explanation:

The force of friction is given by

where is the coefficient of friction and is the normal force.

When the student pulls on the block with force at an angle , the normal force on the block becomes

and hence the frictional force becomes

.

Now, as we increase , increases which as a result decreases the normal force , which also means the frictional force decreases; Hence choice B stands true.

P.S: Choice D is tempting but incorrect since the weight is independent of the external forces on the block.

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