Question

Calculate the magnitude of the normal force on a 15.2 kg block in the following circumstances. (Enter your answers in N.) HINT (a) The block is resting on a level surface. 15.2 Incorrect: Your answer is incorrect. N (b) The block is resting on a surface tilted up at a 25.8° angle with respect to the horizontal. 13.16 Incorrect: Your answer is incorrect. N (c) The block is resting on the floor of an elevator that is accelerating downward at 2.53 m/s2. N (d) The block is on a level surface and a force of 155 N is exerted on it at an angle of 25.8° above the horizontal.

Answer 1

Explanation:

Given that,

Mass of block = 15.2 kg

(a). The block is resting on a level surface.

We need to calculate the force

Using formula of force

$N = mg$

Put the value into the formula

$N=15.2\times9.8$

$N=148.96\ N$

(b). The block is resting on a surface tilted up at a 25.8° angle with respect to the horizontal.

We need to calculate the horizontal force

Using horizontal component

$N=mg\cos\theta$

put the value into the formula

$N = 15.2\times9.8\tinmes\cos(25.8)$

$N=134.11\ N$

(c). The block is resting on the floor of an elevator that is accelerating downward at 2.53 m/s²

We need to calculate the force

Using balance equation

$N-mg=F$

$N=m(g+a)$

Put the value into the formula

$N=15.2\times(9.8+2.53)$

$N=187.4\ n$

(d). The block is on a level surface and a force of 155 N is exerted on it at an angle of 25.8° above the horizontal.

According to FBD,

We need to calculate the force

$N+F\sin\theta=mg$

$N=mg-F\sin\theta$

Put the value into the formula

$N=15.2\times9.8-155\sin(25.8)$

$N=81.49\ N$

Hence, This is the required solution.

Answer 2

The magnitude of the normal force on the 15.2kg for each of the given scenarios are;

A) N = 148.96 N

A) N = 148.96 NB) N = 134.064 N

A) N = 148.96 NB) N = 134.064 NC) N = 187.416 N

A) N = 148.96 NB) N = 134.064 NC) N = 187.416 ND) N = 81.5 N

A) We are told that the mass is 15.2 kg.

Thus; m = 15.2 kg

If the block is resting on a level surface, then the normal force acts opposite to it's weight and as such;

N - mg = 0

N = mg

N = 15.2 × 9.8

N = 148.96 N

B) We are told the block is resting on a surface tilted up at a 25.8° angle with respect to the horizontal.

Thus, resolving the force in the horizontal direction will give us the normal force as;

N = mg cos 25.8°

N = 148.96 × 0.9

N = 134.064 N

C) We are told that the block is resting on the floor of an elevator that is accelerating downward at 2.53 m/s².

Since acceleration is downwards then it means both the downward force and weight will be opposite the normal force. Thus,summation of forces gives;

N - mg - ma = 0

N = m(g + a)

N = 15.2(9.8 + 2.53)

N = 15.2 × 12.33

N = 187.416 N

D) The block is on a level surface and a force of 155 N is exerted on it at an angle of 25.8° above the horizontal.

Since the force of 155 N is acting at angle above the horizontal, then it means it's vertical component acts in the same direction as the normal force. Thus;

N + F sin 25.8 - mg = 0

Thus;

N = mg - 155 sin 25.8

N = 148.96 - 67.46

N = 81.5 N

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